Question

The square of an irrational number is always rational.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Let us consider irrational numbers `sqrt(2)` and `root(4)(2)`

1. `(sqrt(2))^2 = 2`, which is a rational number.
2. `(root(4)(2))^2 = sqrt(2)`, which is an irrational number.

Hence, square of an irrational number is not always a rational number.