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

1 Answer
Sep 26, 2016

Answer:

#=(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#