Question 601215


{{{sqrt(36*x^5*y^6)}}} Start with the given expression.



{{{sqrt(36*x^2*x^2*x*y^6)}}} Factor {{{x^5}}} into {{{x^2*x^2*x}}}



{{{sqrt(36*x^2*x^2*x*y^2*y^2*y^2)}}} Factor {{{y^6}}} into {{{y^2*y^2*y^2}}}



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



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



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



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



{{{6x^2y^3*sqrt(x)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(36*x^5*y^6)}}} simplifies to {{{6x^2y^3*sqrt(x)}}}



In other words, {{{sqrt(36*x^5*y^6)=6x^2y^3*sqrt(x)}}} where every variable is non-negative.