Question

How do you describe how you can estimate the square root of a number that isn't a perfect square without a calculator?

Answer 1

https://www.quora.com/How-do-I-find-the-square-root-of-a-number-which-is-not-a-perfect-square

Answer 2

you can estimate using linear interpolation. For example, if you want the square root of 28, note that 28 is 3/11 of the way from 25(5^2) to 36(6^2).

So, the root will be somewhere near 3/11 of the way from 5 to 6.
3/11 = 0.27, so expect √28 to be about 5.27

In fact, √28 = 5.2915