Question

$\sqrt{108}$simplest radical form

Answer 1

In order to find the simplest radical form, we first need to factorate the number inside the square root. So we have that:

$108=2\cdot2\cdot3\cdot3\cdot3$

Then we will need to use the following property:

$\sqrt[c]{a^b}=a^{}\sqrt[c]{a^{b-c}},\text{ b>c}$

So we have that:

$\sqrt[]{108}=\sqrt[]{2\cdot2\cdot3\cdot3\cdot3}=\sqrt[]{2^2\cdot3^3}=2\cdot3\sqrt[]{2^03^1}=6\sqrt[]{3}$

So the simplest radical form of √108 is 6√3.