Question

A pair of irrational numbers whose product is a rational number is:

• A. $\sqrt{16},\sqrt{4}$
• B. $\sqrt{5},\sqrt{2}$
• C. $\sqrt{3},\sqrt{27}$
• D. $\sqrt{36},\sqrt{2}$

Answer 1

The correct option is C $\sqrt{3},\sqrt{27}$

In the given options,

for option $\left(A\right)$ $\sqrt{16}\&\sqrt{4}$ are not irrational numbers i.e. their real values are 4 & 2 respectively. It cannot be correct answer.

Now multiplying other options, we get

$\left(B\right):\sqrt{5}\times \sqrt{2}=\sqrt{10}$

$\left(C\right)\sqrt{27}\times \sqrt{3}=\sqrt{81}=9$

$\left(D\right)\sqrt{36}\times \sqrt{2}=\sqrt{72}$

So, correct answer is option C.