Question 190506


{{{sqrt(128*x^5*y^3)}}} Start with the given expression.



{{{sqrt(64*2*x^5*y^3)}}} Factor {{{128}}} into {{{64*2}}}



{{{sqrt(64*2*x^2*x^2*x*y^3)}}} Factor {{{x^5}}} into {{{x^2*x^2*x}}}



{{{sqrt(64*2*x^2*x^2*x*y^2*y)}}} Factor {{{y^3}}} into {{{y^2*y}}}



{{{sqrt(64)*sqrt(2)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{8*sqrt(2)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{64}}} to get {{{8}}}.



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



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



{{{8x^2y*sqrt(2xy)}}} Rearrange and multiply.


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Answer:



So {{{sqrt(128*x^5*y^3)}}} simplifies to {{{8x^2y*sqrt(2xy)}}}



In other words, {{{sqrt(128*x^5*y^3)=8x^2y*sqrt(2xy)}}} where every variable is non-negative.