How do i find the square root of something without using a calculator?

Question

can you use 45 as the example

Answer 1

As first answerer was implying, there are advanced ways to do this, but one way is simply to guess, then take the answers that you come up with and take the halfway position between the highest and lowest guess.

First guess: 6*6=36, and 7*7=49, so guess little more than 6.5

6.6^2 = 43.56

Then guess halfway to 7, 6.8:

6.8^2 = 46.24

Too high, so halfway down, 6.7:

6.7^2 = 44.89

too low, halfway up:

6.75^2 = 45.5625

too high:

6.725^2 = 45.226

too high:

6.712^2 = 45.051

too high:

6.706^2 = 44.970

too low:

6.709^2 = 45.011

This isn't the fastest way, but it will work, and get as close as you want.

Answer 2

There's an algorithm for doing just that; it's similar to long division.

Example: find the square root of 169.

(We know the answer is 13, but let's work it out using the algorithm).

Beginning at the decimal point, divide the number into groups of two (169 = 1  69.)

. . . . . . . .________

. . . . . . .V  1   69.

You start with the one. What is it's square root (to the nearest integer)? It's 1, so 1 x 1 = 1. Put a 1 above the bar. Subtract that from 1 and get 0. Then we bring down the 69. Then wed ouble our first factor (1) to get 2. The question now is: what digit X makes 2X x X closest to 69 (without going over, just like long division)? How about 23 x 3; gee, that's 69. So we subtract 69 from 69 and we get 0.

Put the 3 above the bar.

. . . . . . ._1_3____

. . . . . .V   1   69.

. . . . . . . .-1__

. . . . . . . . 0 . .69

. . . . . . . . . . .-69 --

. . . . . . . . . . . . .0

Answer 3

This is really deep math.  usually, people jsut estimate.  but if you want, i can tell you (i'm not undermining you... just don't want to waste your time).

http://www.homeschoolmath.net/teaching/s...