Question 283581


{{{sqrt(144*z^8)}}} Start with the given expression.



{{{sqrt(144*z^2*z^2*z^2*z^2)}}} Factor {{{z^8}}} into {{{z^2*z^2*z^2*z^2}}}



{{{sqrt(144)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{12*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)*sqrt(z^2)}}} Take the square root of {{{144}}} to get {{{12}}}.



{{{12*z*z*z*z}}} Take the square root of {{{z^2}}} to get {{{z}}}.



{{{12z^4}}} Multiply.


==================================================


Answer:



So {{{sqrt(144*z^8)}}} simplifies to {{{12z^4}}}



In other words, {{{sqrt(144*z^8)=12z^4}}} where {{{z>=0}}}.