Question

For $\sqrt{3}{x}^2$ to be irrational, x should be

• A. irrational or rational.
• B. cannot be determined.
• C. always rational.
• D. always irrational.

Answer 1

The correct option is A

irrational or rational.

Let's assume x = $2-\sqrt{3}$
$\Rightarrow \sqrt{3}{x}^2=\sqrt{3}({2-\sqrt{3})}^2$ which is irrational.
Again, assume $x=2$
$\Rightarrow \sqrt{3}{x}^2=\sqrt{3}({2)}^2$ which is also irrational.