Question

Find the square root of $2116$ by prime factorization method

Answer 1

Solve for the square root of given number

Given number is $2116$

$\therefore$Prime factors of $2116$ are

$$\begin{gathered} 2116=2\times 1058 \\ =2\times 2\times 529 \\ =2\times 2\times 23\times 23 \end{gathered}$$

$\therefore 2116=2\times 2\times 23\times 23$

Taking Square root on both sides

$\Rightarrow \sqrt{2116}=\sqrt{2\times 2\times 23\times 23}$

$$\begin{gathered} \Rightarrow \sqrt{2116}=23\times 2 \\ \therefore \sqrt{2116}=46 \end{gathered}$$

Hence the square root of $2116$ is $46$