Question

What will be the number of digits in the square root of 1296?

Answer 1

The number of digits in 1296 is four, which implies that the number of digits in the root must be 2.

Also, the last digit being 6,we have only two options for unit's place in the square root, namely 4 and 6.

Again, 3 times 3 is 9(less than 12 and at the same time close enough to be a accurate) and4 times 4 is 16,so we can be pretty sure the one's digit is 3.

Now out of 34 and 36,the latter is divisible by 3, readily verified. Also 1296 is divisible by 3.

Thus it stands to reason, without much calculation,that if 1296 is a perfect square, then you can be pretty sure its square root is 36.

(the condition of perfect squares does hamper the utility of the method to suit the general purpose, but this is the best I could do I guess.)

Answer 2

2 digit2 digit will be in roof of 1296
It was 36