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
