Question

Find the square root of $90$ in radical form.

Answer 1

Solve for the square root of given number

As we know, a radical form is an expression that contains the radical sign $\left(\sqrt{}\right)$ and the radicand or any number under the radical sign does not contain any perfect square or cube

Given number is $90$.

The prime factorization of $90$ is,

$$\begin{gathered} 90=2\times 45 \\ =2\times 5\times 9 \\ =2\times 5\times 3\times 3 \end{gathered}$$

$\therefore 90=2\times 3\times 3\times 5$

Applying square root on both sides,

$$\begin{gathered} \therefore \sqrt{90}=\sqrt{2\times 3\times 3\times 5} \\ =3\sqrt{10} \end{gathered}$$

Hence, the square root of $90$ in radical form is $3\sqrt{10}$.