We have to prove that
is irrational. We can prove this statement by contradiction.
Let us assume that
is a rational number. Therefore, we can express:

Let us represent this equation as:

Upon squaring both the sides:

Since a has been assumed to be rational, therefore,
must as well be rational.
But we know that
is irrational, therefore, from equation
the expression
must be irrational, which contradicts with our claim.
Therefore, by contradiction,
is irrational.