Question

Determine whether the number is a perfect square 47

Answer 1

No, 47 is not a perfect square.

because a perfect square is a product of a rational multiplied by itself, or a product of a rational number squared. so this means that 47 is not a perfect square because it's not a product of a rational number squared, the closest perfect square is 49, which is 7 multiplied by itself.

Answer 2

perfect squares are n² where n is a whole number
whole numbers are like 0,1,2,3,4,5,6, etc
no decimal or fractions

we can do that be looking at the perfect squares we know
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
etc

so we see 47 is between 6² and 7²
therefor, for n²=47, n is between 6 and 7 and is therfore not a whole number
that makes 47 not a perfect square