Question

Square root of 65 lies between which two numbers (not more than one decimal point)?

Answer 1

Square root of 65 lies between 8.0 and 8.1.

Explanation:

Squares of natural numbers are {1,4,9,16,25,36,49,64,81,...}, which are squares of {1,2,3,4,5,6,7,8,9,....}

As 65 lies between 64 and 81, square root of 65 lies between 8 and 9

Further, $$8.1^2 = 65.61$$ and as $$8.0^2 = 64$$

Thus, square root of 65 lies between 8.0 and 8.1.