Question 294173

{{{sqrt(12*z^10)}}} Start with the given expression.



{{{sqrt(4*3*z^10)}}} Factor {{{12}}} into {{{4*3}}}



{{{sqrt(4*3*(z^5)^2)}}} Rewrite {{{z^10}}} into {{{(z^5)^2}}}



{{{sqrt(4)*sqrt(3)*sqrt((z^5)^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{2*sqrt(3)*sqrt((z^5)^2)}}} Take the square root of {{{4}}} to get {{{2}}}.



{{{2z^5*sqrt(3)}}} Take the square root of {{{(z^5)^2}}} to get {{{z^5}}} and rearrange the terms.


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Answer:



So {{{sqrt(12*z^10)}}} simplifies to {{{2z^5*sqrt(3)}}}



In other words, {{{sqrt(12*z^10)=2z^5*sqrt(3)}}} where {{{z>=0}}}.