√(108)simplest radical form

Question

`√(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.