Question

What's the square root of $625$?

Answer 1

The square root of the given number.

Divide $625$ by $5$,

$625÷5=125$

Divide $125$ by $5$,
$125÷5=25$

Divide $25$ by $5$,

$25÷5=5$

Divide $5$ by $5$,

$5÷5=1$

By using the prime factorization method, $625$ can be written as,

$\therefore 625=5\times 5\times 5\times 5$

Take square root on both sides.

$$\begin{gathered} \sqrt{625}=\sqrt{(5\times 5)\times (5\times 5)} \\ \Rightarrow \sqrt{625}=5\times 5\left(\mathrm{From}\mathrm{each}\mathrm{pair},\mathrm{take}\mathrm{one}\right) \\ \therefore \sqrt{625}=25 \end{gathered}$$

Hence, the square root of $625$ is $25$.