Question

What is the square root of $32$over $4$, expressed in the simplest radical form?

Answer 1

Determine the square root of $32$over$4$, expressed in the simplest radical form.

The square root of a number is the value that returns the original number when multiplied by itself.

Find the prime factors of$\frac{32}{4}$:

$\frac{32}{4}=\frac{2\times 4\times 4}{2\times 2}$

Take square root from both sides of the above equation:

$$\begin{gathered} \sqrt{\frac{32}{4}}=\sqrt{\frac{2\times 4\times 4}{2\times 2}} \\ \Rightarrow \sqrt{\frac{32}{4}}=\frac{\sqrt{2\times 4\times 4}}{\sqrt{2\times 2}} \\ \Rightarrow \sqrt{\frac{32}{4}}=\frac{4}{2}\sqrt{2} \\ \Rightarrow \sqrt{\frac{32}{4}}=2\sqrt{2} \end{gathered}$$

Hence, the square root of $32$over$4$, expressed in the simplest radical form is$2\sqrt{2}$.