Question 294178

{{{sqrt(18*y*z^2)}}} Start with the given expression.



{{{sqrt(9*2*y*z^2)}}} Factor {{{18}}} into {{{9*2}}}



{{{sqrt(9)*sqrt(2)*sqrt(y)*sqrt(z^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{3*sqrt(2)*sqrt(y)*sqrt(z^2)}}} Take the square root of {{{9}}} to get {{{3}}}.



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



{{{3z*sqrt(2y)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(18*y*z^2)}}} simplifies to {{{3z*sqrt(2y)}}}



In other words, {{{sqrt(18*y*z^2)=3z*sqrt(2y)}}} where every variable is non-negative.