Are there any irrational numbers that are perfect squares? If not why? Prove?

Answer 1

No.
An irrational number cannot be expressed as a/b [b<> 0].
Since an irrational number never ends its square root can never end and is also irrational.

Perfect square need not be integers. For example, 1/4 is a perfect square whose square root is 1/2.

Answer 2

A number is known as a perfect square when its square root is an integer.
Integers are all rational.
Therefore all perfect squares are rational.