Question

Find the root of $7744$ by the Prime Factorisation Method.

Answer 1

Find the square root by prime factorisation method:

Given number, $7744$

Factorisation,

$\therefore 7744=2\times 2\times 2\times 2\times 2\times 2\times 11\times 11$

So, the square root of $7744$ is

$$\begin{gathered} 7744=2\times 2\times 2\times 2\times 2\times 2\times 11\times 11 \\ \Rightarrow \sqrt{7744}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 11\times 11} \\ \Rightarrow \sqrt{7744}=2\times 2\times 2\times 11 \\ \therefore \sqrt{7744}=88 \end{gathered}$$

Hence, the square root of $7744$ is $88$.