What is the relationship between perfect squares and square roots examples?

Answer 1

There is a partial relationship.

The principal square root of a perfect square is the number itself.

For example,

the principal square root of 5^2

= the principal square root of 25

= the positive element in {-5, 5}

= 5.

The converse is not true. The number 3, for example, has a square root which are approx -1.7321 and 1.7321. But the square of either of these numbers is 3, but that is not a perfect square since it is not the square of an integer.