Question

Which one is the correct square root of $363$.

• A. $3\sqrt{11}$
• B. $11\sqrt{3}$
• C. $11\sqrt{2}$
• D. none of these

Answer 1

The correct option is B

$11\sqrt{3}$

We have to find the square root of $363$, but we know that $363$ is not a perfect square.

So, By prime factorization, we get

$363=11\times 11\times 3$

Taking square root on both sides, we get

$$\begin{gathered} \sqrt{363}=\sqrt{11\times 11\times 3} \\ =11\sqrt{3} \end{gathered}$$

Hence option B is the correct answer.