Question

If $p$ and $q$ both are perfect squares, then $\sqrt{\frac{p}{q}}$ is always a rational number. Is the statement true?

• A. Yes
• B. No
• C. Cannot be determined
• D. None of these

Answer 1

The correct option is A Yes

if $p$ and $q$ are perfect squares, then we can write

$p=x^2$ and $q=y^2$

$\sqrt{\frac{p}{q}}=\sqrt{\frac{x^2}{y^2}}$

$=\frac{x}{y}$

$=$ a rational number.

So, the given statement is true .