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).

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