How do you simplify #sqrt(27x^4 )#?

1 Answer
Bill K.
Oct 5, 2015

#3sqrt(3)x^2#

Explanation:

First, note that #sqrt(27x^4)=sqrt(27)*sqrt(x^4)#. Next, since #27=9*3=3^2*3#, we can say #sqrt(27)=sqrt(9*3)=sqrt(9)*sqrt(3)=3*sqrt(3)#.

Also, #sqrt(x^4)=sqrt((x^2)^2)=x^2# (in general, #sqrt(y^2)=|y|#, but if #y=x^2#, then #y\geq 0# anyway so we can get rid of the absolute value sign).

Related questions
See all questions in Simplification of Radical Expressions
Impact of this question
3068 views around the world
You can reuse this answer
Creative Commons License