Question

Why are 1 4 9 16 and 25 called perfect squares

Answer 1

Because they are squares of integer numbers.

$1=1^2\\ 4=2^2\\ 9=3^2\\ 16=4^2\\ 25=5^2$

Answer 2

Perfect squares can be divided and multiplied by the same number to get the same number. For example 25/5=5. 5*5=25.
4/2=2, 2*2=4
1/1=1, 1*1=1
9/3=3, 3*3=9
16/4=4, 4*4=16.
Hence the perfect squares.