Question

What is the square root of $108$ in the simplest radical form?

Answer 1

Determine the square root of $108$ in the simplest radical form.

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

The prime factorization of $108$ can be written as:

$108=2\times 2\times 3\times 3\times 3$

Take the square root from both sides of the above value:

$$\begin{gathered} \sqrt{108}=\sqrt{2\times 2\times 3\times 3\times 3} \\ \Rightarrow \sqrt{108}=2\times 3\times \sqrt{3}(\because \surd 3=1.732) \\ \Rightarrow \sqrt{108}=2\times 3\times 1.732 \\ \Rightarrow \sqrt{108}=10.392 \end{gathered}$$

Hence, the square root of $108$ in the simplest radical form is$“10.392”$.