# Formula To Calculate Square Root

**Formula To Calculate Square Root** – Yesterday I was calculating expenses when I noticed the square root button and the memory of calculating the square root by hand struck me.

I believe it was in 8th grade math. It is not covered in Algebra, Geometry, Trig, or PreCalc. At least I don’t think so. We taught the method, but not the theory – perhaps the theory is too complex to absorb at our current level of mathematical education.

## Formula To Calculate Square Root

However, being easily distracted, I put down my calculations and decided to prove to myself that even though I hadn’t used the information in nearly sixty years, I could still do it. I grabbed a pen and paper and randomly picked a four digit number (3,346) and got to work.

#### Square And Cube Roots Of Real Numbers

I was surprised that I figured it out right away. I wrote the number down, circled it with the square root symbol, and began doing it routinely throughout my life. Here is my calculation. The original piece was a bit sloppy, so I copied it more neatly.

(1) You start with a number and after the decimal point in both directions mark every other number with an apostrophe. Obviously, the integer has nothing but zeros to the right of the decimal point.

(2) Find which square of the whole number is equal to or less than the one- or two-digit number, starting from the leftmost. In this case it is 5 because 6 squared is greater than 33. Place this number on the solution line above 33.

(3) Square the number, in this case: 25, and subtract it from the number 33 and subtract “46” in the long division, except that you subtract two numbers. This gives you 846.

## How To Find The Square Root Of 196?” (square Root Of 196 Simplified)

(4) Now multiply the partial answer you have reached so far (5) by 20 to get 100. Find which number multiplied by 100 is closest to 846 and does not exceed that number – and do this calculation. The options are 1 x 101, 2 x 102, 3 x 103, etc. In this case, the correct number is 7. Subtract the answer (749) from 846 and subtract the “00” next to the result – like long division.

(5) Multiply the new partial answer (57) by 20 and continue as above – the result is 1148 x 8 and so on and so forth. Continue the process with as many decimal places as you need in your answer. In the case of 3,346, the decimal string goes to infinity – so I stopped at six.

This information is completely useless today. We need to load a number and click or press the square root key on our phone calculator or handheld calculator or on our computer, and

– Quick answer. But of course, in the primitive days of my school days, our only option was to find an approximation from a slide rule or calculate as above. We use cookies to improve. By using our site, you accept our cookie policy.cookie settings

### Openalgebra.com: Solve By Extracting Square Roots

This article was written by David Zia. David Jia is an academic tutor and founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. David has over 10 years of teaching experience working with students of all ages and grades on a variety of topics including college counseling and test preparation for the SAT, ACT, ISEE and more. After scoring a perfect 800 in math and 690 in English on the SAT, David received a Dickinson Scholarship from the University of Miami, where he earned a bachelor’s degree in business administration. In addition, David has worked as an online video instructor for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

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In the days before calculators, students and professors had to calculate square roots by hand. Several different methods have been developed to tackle this daunting process, some giving a rough estimate, others an exact value. If you want to learn how to find the square root of a number with simple steps, start with step 1 below.

This article was written by David Zia. David Jia is an academic tutor and founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. David has over 10 years of teaching experience working with students of all ages and grades on a variety of topics including college counseling and test preparation for the SAT, ACT, ISEE and more. After scoring a perfect 800 in math and 690 in English on the SAT, David received a Dickinson Scholarship from the University of Miami, where he earned a bachelor’s degree in business administration. In addition, David has worked as an online video instructor for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. This article has been viewed 2,420,004 times.

#### Solving Radical Equations

To calculate the square root by hand, first estimate the answer by finding 2 perfect square roots with the number between them. A perfect square root is any square root of an integer. For example, if you are trying to find the square root of 7, you must first find the first perfect square below 7, which is 4, and the first perfect square above 7, which is 9. Then find the square root of each perfect square. The square root of 4 is 2 and the square root of 9 is 3. So you know that the square root of 7 is somewhere between 2 and 3. Now divide your number by one of the perfect square roots you find. For example, you divide 7 by 2 or 3. If you choose 3, your answer is 2.33. Next, find the average and perfect square root of this number. To get the average in this example, add 2.33 and 2, then divide by 2 to get 2.16. Repeat the process using the average you obtained. First divide the number whose mean square root you are trying to find. Then find the mean and root mean of that number by adding them together and dividing by 2. For example, you first divide 7, the number you started with, by 2.16 and get the calculated average and 3.24. Then you add the old average from 3.24 to 2.16 and divide by 2 to get the new average which is 2.7. Now multiply your answer by itself to see how close it is to the square root of the number you started with. In this example, 2.7 multiplied by itself is 7.29, which is 0.29 different from 7. To get closer to 7, repeat the process. Keep dividing the number you started with by the average of that number and the perfect square, use that number and the old average to find the new average, and multiply the new average by itself until it equals your starting number. If you want to know how to use the long division algorithm to find the square root, keep reading! If you like this site about solving math problems, please report it to Google by clicking the +1 button. If you like this page, please click the +1 button too.

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#### Square Root Of 2

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