Question

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

Answer 1

`sqrt(108)=color(blue)(6sqrt(3))`

Explanation:

Decomposing `108` into factors one step at a time:
`108`
`color(white)("XXX")=2xx54`
`color(white)("XXX")=2xx2xx27`
`color(white)("XXX")=2xx2xx3xx9`
`color(white)("XXX")=2xx2xx3xx3xx3`
`color(white)("XXX")=2^2xx3^2xx3`

`sqrt(108) =sqrt(2^2xx3^2xx3)`
`color(white)("XXX")=sqrt(2^2)xxsqrt(3^2)xxsqrt(3)`
`color(white)("XXX")=2xx3xxsqrt(3)`
`color(white)("XXX")=6sqrt(3)`