Question

Find a square root of $5929$ by prime factorization?

Answer 1

Compute the required value:

We can write,

$5929=7\times 7\times 11\times 11$

Taking square root on both sides,

$$\begin{gathered} \Rightarrow \sqrt{5929}=\sqrt{7\times 7\times 11\times 11} \\ \Rightarrow \sqrt{5929}=\sqrt{7^2\times {11}^2} \\ \Rightarrow \sqrt{5929}=7\times 11 \\ \Rightarrow \sqrt{5929}=77 \end{gathered}$$

Hence, the square root of $5929$ is $77$.