Question 222738


{{{sqrt(72*x^2*y^3)}}} Start with the given expression.



{{{sqrt(36*2*x^2*y^3)}}} Factor {{{72}}} into {{{36*2}}}



{{{sqrt(36*2*x^2*y^2*y)}}} Factor {{{y^3}}} into {{{y^2*y}}}



{{{sqrt(36)*sqrt(2)*sqrt(x^2)*sqrt(y^2)*sqrt(y)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{6*sqrt(2)*sqrt(x^2)*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{36}}} to get {{{6}}}.



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



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



{{{6xy*sqrt(2y)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(72*x^2*y^3)}}} simplifies to {{{6xy*sqrt(2y)}}}



In other words, {{{sqrt(72*x^2*y^3)=6xy*sqrt(2y)}}} where every variable is non-negative.