Question

Product of which of the following number is a rational numbers ?

• A. $p=\sqrt{7}$ and $q=\sqrt{8}$
• B. $p=\sqrt{1}6$ and $q=\sqrt{9}$
• C. $p=2$ and $q=\sqrt{3}$
• D. None of the above

Answer 1

The correct option is B $p=\sqrt{1}6$ and $q=\sqrt{9}$

For option $A$
$pq=\sqrt{7}\times \sqrt{8}=\sqrt{7}\times 2\sqrt{2}=2\sqrt{1}4$
which is irrational
For option $B$
$pq=\sqrt{1}6\times \sqrt{9}=4\times 3=12$
which is rational
So option $B$ is correct.