The Square and the Root

Answer: 0


Finding the square and square root of 49 (least efficient method)
7$\times$7 = 49 so the square root of 49 is 7.

49$\times$49 = 2401

2401$\div$7=343 remainder 0


Finding the square root of 49 but not the square
7$\times$7 = 49 so the square root of 49 is 7.

So 49$\times$49 = 7$\times$7$\times$7$\times$7, which is clearly a multiple of 7.

So the remainder is 0.


The most efficient method - finding neither of the numbers
The square root of 49 multiplied by itself is 49, so 49 is a multiple of the square root of 49.

So multiples of 49 are also multiples of the square root of 49.
49 squared is a multiple of 49.
So 49 squared is also a multiple of the square root of 49.
So the remainder when the square of 49 is divided by the square root of 49 is 0.