Question

What's the square root of $729$ ?

Answer 1

The square root of the given number.

By using the prime factorization method, $729$ can be written as,

$\therefore 729=3\times 3\times 3\times 3\times 3\times 3$

Take square root on both sides.

$$\begin{gathered} \sqrt{729}=\sqrt{(3\times 3)\times (3\times 3)\times (3\times 3)} \\ \Rightarrow \sqrt{729}=3\times 3\times 3\left(\mathrm{From}\mathrm{each}\mathrm{pair},\mathrm{take}\mathrm{one}\right) \\ \Rightarrow \sqrt{729}=27 \end{gathered}$$

Hence, the square root of $729$ is $27$.