Question

How do you simplify `sqrt(27/p^2)`?

Answer 1

`=(3sqrt(3))/p`

Explanation:

Write the values under the root in factor form, trying to make squares where possible.

Find the square roots where you can.

#sqrt(27/p^2) = sqrt((3xx9)/p^2) =sqrt(3xx3^2xxp^-2#
=`sqrt(3)xxsqrt(3^2)xxsqrt((p^-1)^2)`

by mathematical definition
`sqrt(3)=sqrt(3)`
`sqrt(3^2)=3`
`sqrt((p^-1)^2)=sqrt((1/p)^2)=1/p`
=`3xx1/psqrt3`
`=(3sqrt(3))/p`