Question

Find the square root of $2401$ with prime factorization.

Answer 1

Given, the number is $2401$.

By prime factorisation,

$2401=7\times 7\times 7\times 7$

Taking square root on both sides, we get

$$\begin{gathered} \sqrt{2401}=\sqrt{7\times 7\times 7\times 7} \\ =7\times 7 \\ =49 \end{gathered}$$

Hence, the square root of $2401$ is $49$.