How do I estimate the square root of a number using the division method?

Answer 1

1. Estimate the square root to at least 1 digit.
2. Divide this estimate into the number whose square root you want to find.
3. Find the average of the quotient and the divisor. The result becomes the new estimate.

Eg:
Finding the square root of 20 using 10 as the initial guess:

Guess Divide Find average
10 20/10 = 2 average 10 and 2 to give new guess of 6
6 20/6 = 3.333 average 3.333 and 6 gives 4.6666
4.666 20/4.666= 4.1414 average 4.666,4.1414= 4.4048
4.4048 20/4.4048=4.5454 average = 4.4700
4.4700 20/4.4700=4.4742 average = 4.4721
4.4721 20/4.4721=4.47217 average = 4.47214
This is already to 4 decimal places
4.47214 20/4.47214=4.472132 average =4.472135
4.472135 20/4.472135=4.472137 average = 4.42136

Answer 2

There is a method called the Babylonian Method that may be what you are looking for. Estimate the square root of N: Start with a guess, n. Compute N/n (divide N by n). Average N/n and n: n'=.5(N/n +n). Repeat the process with n', and so on.

Answer 3

that's something extra effective, all of us comprehend the sq. root is going to end in 5. something else of the volume is going to be stumbled on by technique of doing right here : x(x + a million) = 182 x^2 + x - 182 = 0 remedy this. note: purely constructive numbers are ideal to sq. roots. you should get one hundred thirty 5 as an answer.

Answer 4

If I didn't have a calculator, I always just used trial and error. It helps to have memorized quite a few squares, up to 20 or so, too. Sorry I can't be of more help.

Answer 5

by multipling it