Using the ratio of perfect squares method, what is square root of 41 rounded to the nearest hundredth?

Do not use your calculator to answer this question. Use the ratio of perfect squares method.

Hello,

I haven't found the ration of perfect squares methode unless it is to know all square root of numbers <100 (by heart)

As 41 is a primer number, I propose you an other old method (de Héron d'alexandrie)

Explanation:

x²=a

==>2x²=x²+a

==>2x = (x²+a) / x

==>2x=x+a/x

==>x = (x+a/x) / 2 that is the recursive formula for the algorithm