# How To Find Fourth Root Without Calculator

So in this case the fourth root of 81 is the square root of the square root of 81. Take the number you wish to find the square root of, and group the digits in pairs starting from the right end. Let me tell you the way out. The square root of 2 is 1. HI EVERYONE I was thinking if we could find a cube root without using a calculator. Sal Romano Oct 28, 2019 at 2:54 AM EDT 0 Comment 0. It is also possible to calculate breakeven revenue directly without calculating breakeven units first. Inverse Laplace Transform by Partial Fraction Expansion. Find Square root Game Online practice for 2nd grade, 3rd grade, 4th grade and 5th grade. You should not take any action on the basis of the information provided through this calculator. Read your Rising Sign as well as your Sun Sign in each Monthly Horoscope Forecast. The four roots x 1, x 2, x 3, and x 4 for the general quartic equation + + + + = with a ≠ 0 are given in the following formula, which is deduced from the one in the section on Ferrari's method by back changing the variables (see § Converting to a depressed quartic) and using the formulas for the quadratic and cubic equations. Type the number, you want to calculate cube root for 2. It is denoted by √ 3. Press square root 12 times 3. If no factor is left out then the number is a perfect cube. If you are on a job interview and are asked to find the square root of a number without using the square root button or exponential function on a calculator, this method (called the Babylonian method) will come in handy. I am looking to calculate what the equivalent daily return should be. Calculate Square Root Without Using Sqrt in C First one, we have to know how to calculate square root without using a function. For example, if you want to find the square root of 16, think which number when multiplied with itself, gives the answer to be 16. Square roots, which use the radical symbol, are nonbinary operations — operations which involve just one number — that ask you, "What number times itself gives you this number under the radical. I tried int(n**(1/k)) But for n=125, k=3 this gives the wrong answer! I happen to know that 5 cubed is 125. Easy for anyone. Take an example of a SQUARE ROOT. We can use the linear approximation to compute any such inverse function to the accuracy that our machine will allow, as we shall see next. Geometric Mean = 4th root of 1100 X 1 X 30 X 13000 = 4th root of 429,000,000 Geometric Mean = 143. Each state has different formulas that they use in determining how to calculate child support. This observation connects to the Fundamental Theorem of Algebra since the equation z 4 = 1 is a fourth-degree equation so must have exactly four roots. This calculator is for a right triangle only! The factors are the lengths of the sides and one of the two angles, other than the right angle. Nth root You are encouraged The 4th root of 16 is 2 For BASICs without the ^ operator, /*NetRexx program to calculate the Nth root of X, with DIGS accuracy. The square root, denoted by a 2 on top of the "root thing" or more commonly without a number at all, is the second root. Use your calculator to calculate cube root 5 and compare that result to the one obtained using Newton's method. The 5th root of 1,024 is 4, as 4 x 4 x 4 x 4 x 4 is 1,204. If we want to calculate square root, we can use Math. Instructions for the roots calculator. UPS's shipping calculator estimates the time and cost of delivery based on the destination and service. This page is about converting a fraction (i. On asking these to my maths teacher , in addition to these he told me that how to take out nth root [if we want to take out 7th root of 128 which is (128)^1/7 =2 ] it can be also done using a simple calculator. There are other ways of working out square roots on this page. A strategy for finding roots. If you’re having turkey, weigh it (once stuffed, if you’re doing so) to calculate the cooking time, allowing 30-35 min per kg (2lb. Sometimes there's a root with an x on/beside it. Precise paint needs will vary according to many factors, including application method. These rules cover all polynomials, and now we add a few rules to deal with other types of nonlinear functions. For checking whether you have learned the topic, think of any number like this, calculate its unit digit and then check it with the help of a calculator. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis. h header file. Finding nth roots of Complex Numbers. It is also possible to calculate breakeven revenue directly without calculating breakeven units first. Ask the spectator to choose any whole number less than 100 and, using a calculator, to find its cube by multiplying the number by itself, then multiplying the answer by the original number. Work through each of the steps to find the standard deviation. copySign() method. So many situations and applications can be modeled or represented by them that a large portion of mathematics taught in high school and college are topics that deal with fucntions. Matlab allows you to create symbolic math expressions. You should not take any action on the basis of the information provided through this calculator. To calculate the square root of an imaginary number, find the square root of the number as if it were a real number (without the i) and then multiply by the square root of i (where the square root of i = 0. And for any negative value a, its fourth roots are not real. The calculation begins. They create a table of perfect squares. Enter value and click on calculate. Direct Calculation (most popular) - a precise, digit by digit calculation similar to long division. Discover more every day. To use the calculator simply type any positive number into the 'enter number' box then type in the 'nth root' you want to find. And so to find 24% of $412, we are taught to change 24% to the decimal. Here's how to install the Android SDK and root your Kindle Fire. To improve your gas mileage you first need to know what your current gas mileage is or you will not know if it got any better. Today, a few buttons pushed, we get the result in no time. You know what? I have found that there are five different ways to calculate a square root in Excel. 24 , and multiply times 412. This is a better choice than 4: 4 × 4 = 16. button, 12 timesyou'll get approx cube root. For example, 2 is the square root of 4, because 2x2=4. The discriminant tells the nature of the roots. When trying to find roots, how far left and right of zero should we go? There is a way to tell, and there are a few calculations to do, but it is all simple arithmetic. This c program code will be opened in a new pop up window once you click pop-up from the right corner. Q: How do I find roots other than square roots using the BAII Plus? In finance it seems that we are forever calculating various roots (cube root, fourth root, 365th root, etc). The text below assumes. Finding Zeros, Roots, Solutions, x-intercepts. There are other ways of working out square roots on this page. How does this cube root calculator work? This cube root calculator might come in handy whenever you need to calculate the cube root of any given positive or negative numbers (including decimals). Radicand: The thing you are finding the root of. Note that the TI 84 Plus does not allow you to specify a day count basis (e. The program can handle even the tricky equations, without you having to make a guess for the root. Enter the root degree (n) and number (x) and press the = button. A Worked Example. On your cheap non-scientific calculator: You will need to be familiar with exponents since your calculator cannot take care of them for you. Want to fix your operating system by reinstalling Windows 10 without losing data? This post will walk you through how to reinstall Windows 10 without CD or USB drive, as well as how to reinstall Windows 10 from a USB drive or with CD. Because that would be too easy. again without using a calculator?? "Newton's method" is good for that general kind of problem. I'm good at maths, when I know how to solve the equation and what it is!. BMI is your weight (in kilograms) over your height squared (in centimeters). The TI graphing calculator can be used to find the real roots of an equation. You can also find real solutions to quadratic equations by graphing them and using the 'zero' function to calculate where the graph intersects the x-axis. In the previous section we introduced the Wronskian to help us determine whether two solutions were a fundamental set of solutions. Polymathlove. Precise paint needs will vary according to many factors, including application method. For example, to find the 17th root of a number, you raise it to the one-seventeenth (1/17) power. For example, use the square root calculator below to find the square root of 7. Square Roots without a calculator! Lots of people have asked us how to get square roots without a calculator, and lots of others have sent us different ways of doing it! You'll find the classic method written out for you in Easy Question Evil Answers. Zeros or roots of functions and solutions to equations can either be real or complex numbers. MilesGallon. All you need to do is find the number that multiplies by itself four times to equal the number you are taking the fourth root of. To calculate the cube root of a number in Excel, use the caret operator (^) with 1/3 as the exponent in a simple formula. You will get the result 4, that is the 4th root of 256 is equal to 4. Voiced by the actors behind Aya and Shiori in Root Letter. Yes, five different methods, which you can use in different situations. If you need to know the square root of a numberthe square root calculator is here to help you. Most people in today's world feel that since calculators can find square roots, that children don't need to learn how to find square roots using any pencil-and-paper method. Determine the annualized interest rate, which is listed in the loan documents. , 30/360 or actual/360). Pythagorean Theorem calculator, formula, work with steps, step by step calculation, real world and practice problems to learn how to find any unknown side length of a right triangle. Perhaps, then, it is this calculator: Let's say you want to take the fifth root of 2. Go to your Kindle's settings page to find out the serial number. 32 = 32(cos0º + isin 0º) in trig form. In certain cases, as is the case with mainframes and minicomputers, our calculation of the cube root is a very close approximation. Free practice questions for SAT Math - How to find the volume of a cylinder. Earlier model TI graphing calculators don't have it built in, but they do have factoring programs. Calculator Plus (C) 2019 Digitalchemy, LLC. You can find the 5th root of 108 by using division and finding 4th roots. 5 as power here. We can use the linear approximation to compute any such inverse function to the accuracy that our machine will allow, as we shall see next. In practical terms. Therefore, you can calculate the minimum grade you need to score on the final exam using the formula: Required = (Goal − Current × (100% − Final Weight)) / Final Weight. How to put square roots into exponents, hyperbola, parabola, inverse square root, square root subtraction calculator, find three pairs of numbers for which the least common multiple equals the product of the two numbers, simplify polynomials common factors, algebra 2 vertex form, what is the formula for subtracting integers. In this related lesson, you will find a derivation of this formula for the period of a simple pendulum that will help you understand the restrictions on its use. Quartiles Calculator Instructions. So, you might want to come up with a dynamic criterion for when to stop. Note that the TI 84 Plus does not allow you to specify a day count basis (e. For example, 2 is the square root of 4, because 2x2=4. For calculate square root of a number, we will use The Babylonian M. It is just too much work otherwise. The problem with using approximations and rounding with numbers on a calculator isn't limited to working with two numbers of very different size. Some suitcases will have handles that stick out even after you have pushed them in as far as they will go. Take an example of a SQUARE ROOT. If an input is given then it can easily show the result for the given number. Radical symbol: The √ symbol that means "root of". Polynomial Regression Online Interface. Given 2809. 32 = 32(cos0º + isin 0º) in trig form. For example, if you want to calculate the square root of 8254129, write it as 8 25 41 29. Note that the TI 84 Plus does not allow you to specify a day count basis (e. Music Theory: Intervals, and How to Derive Them From D to up G is a perfect 4th, and so on. The first sqrt number should be the input number / 2. 3 Minimum Spanning Trees. Scientific Calculator. The inverse function of any of the trig functions will return the angle either measured in degrees or radians. "exponents" + worksheet + simplify + negative, simplfying fractions test, solve online second grade equation. LCM is the smallest number that is multiple of two or more numbers. Note that calculators or computers are used for most square root calculations, but knowing how to manually calculate a square root can be quite useful when no calculator is available. Aortic Root Z-Score Calculator Data Input Form Z-scores of the aortic root (aortic annulus, sinuses of Valsalva, sinotubular junction, and ascending aorta) are commonly reported for conditions such as Marfan syndrome, bicuspid aortic valve, and Kawasaki disease. image/svg+xml. I know I sound stupid, I'm just started out though & did GCSE maths a while back. To calculate the square root of an imaginary number, find the square root of the number as if it were a real number (without the i) and then multiply by the square root of i (where the square root of i = 0. A graphing calculator follows order of operations when performing a computation. 01 critical values for the Studentized range statistic Q. Squaring a number and taking a square root are very common operations in mathematics. Finding square roots and converting them to exponents is a relatively common operation in algebra. nextAfter() method. e Worksheet by Kuta Software LLC. Enter your kindle serial number below and it will compute your password. While the value is an approximation, especially for real gases, it offers useful information when studying kinetic theory. Simplify ∜512. i am new in Java. Hence, to the nearest degree, θ = 180° − 50° = 130° or θ = 360° − 50° = 310°. For example: 3 is a square root of 9, since 3 2 = 9. Anything wrong with your Windows 10 could cause your PC to run slowly and even stop it from working properly. Calculations can be performed using either Python or VBScript. with different values, you will find that sometimes the routine converges faster and sometimes it takes longer. Press Multiply and then equal to. 70997594 is a good approximation to cube root 5. ) can also be used to find a minimum or maximum of such a function, by finding a zero in the function's first derivative, see Newton's method as an optimization algorithm. Learning how to factor polynomials does not have to be difficult. Use this calculator to find the fourth root of a number. Find the value of 125^1/3 (I can't make that 1/3 tiny in the corner on my screen). Symbolic Math in Matlab. m a √ = b if bm = a. The following examples show full details. The length of the horizontal bar is important. Like, for example, A B C. In practical terms. It also factors polynomials, plots polynomial solution sets and inequalities and more. The calculation begins. This may seem like a useless idea. The second way uses the key. 06 (x n) using a calculator allowed in the CA/CWA/CS examination hall. News About How to Calculate HRA from Basic. Calculate hours worked using our online time card calculator - Try it! It's simple and easy to use. Properties of Square Roots and Radicals. Roots are also called x-intercepts or zeros. Square root fraction calculator (radicals quotient) The online calculator of square root can calculate online square root quotients in exact form. equation: x to the fourth power - 16 = 0 ( )( )= 0 conjugates. If you’re having turkey, weigh it (once stuffed, if you’re doing so) to calculate the cooking time, allowing 30-35 min per kg (2lb. These rules cover all polynomials, and now we add a few rules to deal with other types of nonlinear functions. You can also calculate other degrees (cube, fourth, ), or do the reverse operation, i. button, 12 timesyou'll get approx cube root. Be sure to use significant figures when rounding your answer. Hence, to the nearest degree, θ = 180° − 50° = 130° or θ = 360° − 50° = 310°. Be informed and get ahead with. Too Many Results?. Square Root Calculator Find In Just One Omni. Is The Keto Diet Safe For High Blood Pressure Keto Diet Plan Bacon How To Calculate Your Macros On A Keto Diet How To Do Keto Diet Without Losing Weight Keto Diet And Skin Glow Before And After. I tried int(n**(1/k)) But for n=125, k=3 this gives the wrong answer! I happen to know that 5 cubed is 125. Conjugate pairs. com happens to be the right site to take a look at!. Also ideas for interviewing relatives. 71828) in your calculator and now press the √ (Square root) key 12 times. Minimum spanning tree. In this video the instructor shows how to simplify radicals. The Root 2020 Presidential Black Power Rankings, Week 15 to be a committee heartbreaker. In the previous section we introduced the Wronskian to help us determine whether two solutions were a fundamental set of solutions. As the inverse of this concept, finding square roots can be done quickly when dealing with whole numbers or in a few simple steps when working with more difficult numbers. 71088435 x 3 = 1. Zero, one or two inflection points. With a cube root calculator, you can find the roots of both positive and negative numbers. Therefore, we need to sketch the following triangle within trapezoid : We know that the base of the triangle has length. Fortunately, this is pretty simple to do if you can remember a simple mathematical rule: $\sqrt[N]{X} = {X^{\frac{1}{N}}}$ So, to calculate the 5th root of 100, we simply raise 100 to the 1/5th power. Suppose you're given the data set 1,2,2,4,6. Lesson Title: Square Roots 2. in the set of real numbers. To do this, multiply both sides of the equation above by price. To find the fourth root of a number, you raise the number to either the one-fourth (1/4) or 0. See note below. The text below assumes. Fourth degree polynomials are also known as quartic polynomials. A neat trick to quickly calculate fifth roots. How I could know the dominant poles of a dynamic control system if I have the transfer function? - calculate the roots of the numerator polynomial Asked 4th Apr, 2015. 06 (x n) using a calculator allowed in the CA/CWA/CS examination hall. For complex or imaginary solutions use Simplify Radical Expressions Calculator. pdf - search pdf books free download Free eBook and manual for Business, Education,Finance, Inspirational, Novel, Religion, Social, Sports, Science, Technology, Holiday, Medical,Daily new PDF ebooks documents ready for. Values must be numeric and may be separated by commas, spaces or new-line. Note that calculators or computers are used for most square root calculations, but knowing how to manually calculate a square root can be quite useful when no calculator is available. Five Ways to Calculate Frequency Distributions in Excel Although Excel's FREQUENCY function was designed to calculate frequency distributions, you also can use the SUM-IF, SUMPRODUCT, INDEX-FREQUENCY, and COUNTIFS functions. Wolfram|Alpha is a great tool for finding polynomial roots and solving systems of equations. Use the interest formula to arrive at the. Grade A will break down the steps for you, show you simple examples with visual illstrations, and also give you some clever tips and tricks. A square root of a number is a number that, when it is multiplied by itself (squared), gives the first number again. If you have a set of grades to calculate, and don’t want to do it by hand, you can use the following form to calculate the grades of your students on a square root curve by entering their grades in the box below. By using Pascal™s Triangle to find the coefficient values of the expanded series of term you want to break down, you can derive a formula to find the nth roots respectively. I can see on SQROOT which gives the square root. Only numbers bigger than or equal to zero have real square roots. Here is that funny long division-like method for finding square and cube roots generalized to nth roots. 71088435 x 3 = 1. Geometric Mean = 4th root of 1100 X 1 X 30 X 13000 = 4th root of 429,000,000 Geometric Mean = 143. Guidelines: Enter you number into the box on top and hit the "Calculate" button. This online calculator is set up specifically to calculate 4th root. Question 167367: Find all the fourth roots of 16. There are 5, 5 th roots of 32 in the set of complex numbers. sqrt() method to find out the square root of any number. Even for perfect nth root numbers, a root can be difficult to. Top 5 Uses For A Scientific Calculator Hp Tech Takes. If there exists such a number, then the number is the. The fourth root of n is a number a such that 4√a = n. So, you might want to come up with a dynamic criterion for when to stop. Solve Equation With Square Roots. For large n, the n th root algorithm is somewhat less efficient since it requires the computation of − at each step, but can be efficiently implemented with a good exponentiation algorithm. Note that the TI 84 Plus does not allow you to specify a day count basis (e. Our cube root calculator is a handy tool that will help you determine the cube root, also called the 3 rd root, of any positive number. Java program to find out square root of a given number Dear all, Please give me a java code for calculate square root without using math function. Press these keys x,= 13 times and you will get the cube root of the number. Use ENTER to finish calculations and to choose menu items. Type in any function derivative to get the solution, steps and graph. This calculator has three ways of entering the root. From YouTube to your favorite podcast app, listen and watch the show anytime, anywhere. The Root of a number is inverse of Power of the number. Radical symbol: The √ symbol that means "root of". exam, this article shows you how to calculate a subnet mask, break down IP address classes and understand binary. To calculate any root of a number use our Nth Root Calculator. Calculate the length, width, height, or volume of a rectangular box. Find your yodel. It gives the measurement on how the numbers of data are distributed about the mean/expected value. y times multiplication of x. Some suitcases will have handles that stick out even after you have pushed them in as far as they will go. Most people in today's world feel that since calculators can find square roots, that children don't need to learn how to find square roots using any pencil-and-paper method. Calculating the degree of a polynomial. So the square. Write a C program to find all roots of a quadratic equation using if else. Just type in any equation you want to solve and Quartic Equation Calculator will show you the result. 022 x 10 23. At every round of the algorithm we use a pair of digits from the number and will find one digit for the answer. For example: 1. Measurements are classified as one dimension, two dimensions or three dimensions. ) can also be used to find a minimum or maximum of such a function, by finding a zero in the function's first derivative, see Newton's method as an optimization algorithm. For a given number "a", the cube root is the number "b" that if multiplied by itself for 3 times equals "a". The nth Root Symbol. Hope this helps Kai-Uwe Bux. Financial Math Formulas and Financial Equations. There are four solutions: 2, -2, i, i. In the fields below, you can specify a word root or some part of its meaning and our site's search engine will try to find matches for you. Note that calculators or computers are used for most square root calculations, but knowing how to manually calculate a square root can be quite useful when no calculator is available. You may also like: Calculate Square Root Without Using Math. How do you calculate the square root to the fifth or square root to the fourth power, etc. So split the number inside the fourth root as the product of two perfect squares and then cancel out the. To find the fourth root of a complex number in polar form we simply take the fourth root of r and divide the angle by 4. From the root locus i need to find the undamped namtural freq, damping ratio and settling time. Algebra Calculator. Suppose you're given the data set 1,2,2,4,6. To find the nth root of a number, raise that number to the power of 1/n. Find the range of square root functions; examples and matched problems with their answers at the bottom of the page. You are here: Home → Lessons & teaching tips Math Lessons and Teaching Tips. Finding The Square Root Of 169. If you don't, there's a logical process you can follow to systematically figure out the square root of any number, even if you. Take the interactive quiz at the bottom of this page to find out how much you've learned. Press Multiply and then equal to. Examples: The 4th root of 81, or 81 radical 3, is written as $$\sqrt{81} = \pm 3$$. In this traversal, we first create links to Inorder successor and print the data using these links, and finally revert the changes to restore original tree. again without using a calculator?? "Newton's method" is good for that general kind of problem. Learn to calculate numbers quickly without a calculator with The List Universe's 10 arithmetic tricks. If you would like to try this method yourself, try finding the square root of 7. This produces the related angle 50° (to the nearest degree). To find the cube root of a number, press , select 4:3 (,. Better use a scientific calculator to do this. This is the standard deviation. Calculating square root is easy if you have a whole number. Top 5 Uses For A Scientific Calculator Hp Tech Takes. If discriminant is less than 0, the roots are complex and different. Time-saving radical expressions video and example problems simplify square, cube, and fourth roots with absolute values and variables. A radical is nothing but another name for a square root. These are all really extensions of the Binomial Theorem. This calculator is designed to give the cube and cube root of any number. They are also known as zeros. Find nutrition facts, including food labels, calories, nutritional information and analysis that helps promote healthy eating by telling you about the foods you eat. Square Root Calculator Find In Just One Omni. If you see the low–power indicator ( ¤) in the display, replace the batteries as soon as possible. Be sure to use significant figures when rounding your answer. This calculator is for a right triangle only! The factors are the lengths of the sides and one of the two angles, other than the right angle. 06 (x n) using a calculator allowed in the CA/CWA/CS examination hall. This includes a Tax Bracket Calculator, W-4 Withholding Calculator, Self-Employed Expense Estimator, Documents Checklist tool, TaxCaster, and more. Show me pay rates as at For pay rates before 1 July 2014. The Quartic equation might have real root or imaginary root to make up a four in total. You only need to enter one of each grades if there are multiples of the same score. The root of that perfect square is the first digit of our root. Step-1: W rite numbers in a row of 4 terms in such a way that the first one is the cube of the 1 st digit, second one is the square of 1 st number multiplied by 2 nd digit, third one is the 1 st digit multiplied by square of 2 nd digit and the fourth one is the cube of the 2 nd digit. Feel free to try it out with your own favorite numbers Search engines can file this page using the following key words: square root, math, algebra, solving, how to find square roots without a calculator, math without calculators, finding square roots, square root algebra, square root arithmetic, roots, squares, solving math problems, math no calculator, no calulator, square root, problem. But now I'm not sure how to interpret my regression coefficients. But for negative or complex numbers, it can be done as follows. In certain cases, as is the case with mainframes and minicomputers, our calculation of the cube root is a very close approximation. From this the equilibrium expression for calculating K c or K p is derived. For example, use the square root calculator below to find the square root of 7. In practical terms. You can do this with all the other moveable chord shapes as well. When a suitcase has rounded corners, measure to where the corners would be if they were not rounded. The fact-checkers, whose work is more and more important for those who prefer facts over lies, police the line between fact and falsehood on a day-to-day basis, and do a great job. Today, my small contribution is to pass along a very good overview that reflects on one of Trump’s favorite overarching falsehoods. Namely: Trump describes an America in which everything was going down the tubes under Obama, which is why we needed Trump to make America great again. And he claims that this project has come to fruition, with America setting records for prosperity under his leadership and guidance. “Obama bad; Trump good” is pretty much his analysis in all areas and measurement of U.S. activity, especially economically. Even if this were true, it would reflect poorly on Trump’s character, but it has the added problem of being false, a big lie made up of many small ones. Personally, I don’t assume that all economic measurements directly reflect the leadership of whoever occupies the Oval Office, nor am I smart enough to figure out what causes what in the economy. But the idea that presidents get the credit or the blame for the economy during their tenure is a political fact of life. Trump, in his adorable, immodest mendacity, not only claims credit for everything good that happens in the economy, but tells people, literally and specifically, that they have to vote for him even if they hate him, because without his guidance, their 401(k) accounts “will go down the tubes.” That would be offensive even if it were true, but it is utterly false. The stock market has been on a 10-year run of steady gains that began in 2009, the year Barack Obama was inaugurated. But why would anyone care about that? It’s only an unarguable, stubborn fact. Still, speaking of facts, there are so many measurements and indicators of how the economy is doing, that those not committed to an honest investigation can find evidence for whatever they want to believe. Trump and his most committed followers want to believe that everything was terrible under Barack Obama and great under Trump. That’s baloney. Anyone who believes that believes something false. And a series of charts and graphs published Monday in the Washington Post and explained by Economics Correspondent Heather Long provides the data that tells the tale. The details are complicated. Click through to the link above and you’ll learn much. But the overview is pretty simply this: The U.S. economy had a major meltdown in the last year of the George W. Bush presidency. Again, I’m not smart enough to know how much of this was Bush’s “fault.” But he had been in office for six years when the trouble started. So, if it’s ever reasonable to hold a president accountable for the performance of the economy, the timeline is bad for Bush. GDP growth went negative. Job growth fell sharply and then went negative. Median household income shrank. The Dow Jones Industrial Average dropped by more than 5,000 points! U.S. manufacturing output plunged, as did average home values, as did average hourly wages, as did measures of consumer confidence and most other indicators of economic health. (Backup for that is contained in the Post piece I linked to above.) Barack Obama inherited that mess of falling numbers, which continued during his first year in office, 2009, as he put in place policies designed to turn it around. By 2010, Obama’s second year, pretty much all of the negative numbers had turned positive. By the time Obama was up for reelection in 2012, all of them were headed in the right direction, which is certainly among the reasons voters gave him a second term by a solid (not landslide) margin. Basically, all of those good numbers continued throughout the second Obama term. The U.S. GDP, probably the single best measure of how the economy is doing, grew by 2.9 percent in 2015, which was Obama’s seventh year in office and was the best GDP growth number since before the crash of the late Bush years. GDP growth slowed to 1.6 percent in 2016, which may have been among the indicators that supported Trump’s campaign-year argument that everything was going to hell and only he could fix it. During the first year of Trump, GDP growth grew to 2.4 percent, which is decent but not great and anyway, a reasonable person would acknowledge that — to the degree that economic performance is to the credit or blame of the president — the performance in the first year of a new president is a mixture of the old and new policies. In Trump’s second year, 2018, the GDP grew 2.9 percent, equaling Obama’s best year, and so far in 2019, the growth rate has fallen to 2.1 percent, a mediocre number and a decline for which Trump presumably accepts no responsibility and blames either Nancy Pelosi, Ilhan Omar or, if he can swing it, Barack Obama. I suppose it’s natural for a president to want to take credit for everything good that happens on his (or someday her) watch, but not the blame for anything bad. Trump is more blatant about this than most. If we judge by his bad but remarkably steady approval ratings (today, according to the average maintained by 538.com, it’s 41.9 approval/ 53.7 disapproval) the pretty-good economy is not winning him new supporters, nor is his constant exaggeration of his accomplishments costing him many old ones). I already offered it above, but the full Washington Post workup of these numbers, and commentary/explanation by economics correspondent Heather Long, are here. On a related matter, if you care about what used to be called fiscal conservatism, which is the belief that federal debt and deficit matter, here’s a New York Times analysis, based on Congressional Budget Office data, suggesting that the annual budget deficit (that’s the amount the government borrows every year reflecting that amount by which federal spending exceeds revenues) which fell steadily during the Obama years, from a peak of$1.4 trillion at the beginning of the Obama administration, to $585 billion in 2016 (Obama’s last year in office), will be back up to$960 billion this fiscal year, and back over \$1 trillion in 2020. (Here’s the New York Times piece detailing those numbers.) Trump is currently floating various tax cuts for the rich and the poor that will presumably worsen those projections, if passed. As the Times piece reported: