Question 191899


{{{sqrt(32*x^5*y^2)}}} Start with the given expression.



{{{sqrt(16*2*x^5*y^2)}}} Factor {{{32}}} into {{{16*2}}}



{{{sqrt(16*2*x^2*x^2*x*y^2)}}} Factor {{{x^5}}} into {{{x^2*x^2*x}}}



{{{sqrt(16)*sqrt(2)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{4*sqrt(2)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)}}} Take the square root of {{{16}}} to get {{{4}}}.



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



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



{{{4x^2y*sqrt(2x)}}} Rearrange and combine the terms.


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Answer:



So {{{sqrt(32*x^5*y^2)}}} simplifies to {{{4x^2y*sqrt(2x)}}}



In other words, {{{sqrt(32*x^5*y^2)=4x^2y*sqrt(2x)}}} where every variable is non-negative.