Question

Find the square root of $8281$ by prime factorization.

Answer 1

Solve for the square root of given number:

Given number is $8281$

$\therefore$By prime factorization method,

$$\begin{gathered} 8281=7\times 1183 \\ =7\times 7\times 169 \\ =7\times 7\times 13\times 13 \end{gathered}$$

$\therefore 8281=7\times 7\times 13\times 13$

Applying square root on both sides, we get,

$\sqrt{8281}=\sqrt{7\times 7\times 13\times 13}$

$=7\times 13$

$=91$

$\therefore \sqrt{8281}=91$

Hence, the square root of $8281$ is $91$.