Question

Find the value of ${\left(64\right)}^{\frac{1}{2}}$

Answer 1

Compute the required value

Given, ${\left(64\right)}^{\frac{1}{2}}$

We know that ,$64=8^2$

$$\begin{gathered} \therefore {\left(64\right)}^{\frac{1}{2}}={\left(8^2\right)}^{\frac{1}{2}} \\ ={\left(8\right)}^{2\times \frac{1}{2}}\left[\because {\left(a^m\right)}^n=a^{m\times n}\right] \\ =8 \\ \Rightarrow {\left(64\right)}^{\frac{1}{2}}=8 \end{gathered}$$

Hence, the value of ${\left(64\right)}^{\frac{1}{2}}$ is $8$