Question 178027

{{{sqrt(25*x^5*y^4)}}} Start with the given expression.



{{{sqrt(25*x^2*x^2*x*y^4)}}} Factor {{{x^5}}} into {{{x^2*x^2*x}}}



{{{sqrt(25*x^2*x^2*x*y^2*y^2)}}} Factor {{{y^4}}} into {{{y^2*y^2}}}



{{{sqrt(25)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{5*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y^2)}}} Take the square root of {{{25}}} to get {{{5}}}.



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



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



{{{5x^2y^2*sqrt(x)}}} Rearrange and multiply.



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Answer:



So {{{sqrt(25*x^5*y^4)}}} simplifies to {{{5x^2y^2*sqrt(x)}}}



In other words, {{{sqrt(25*x^5*y^4)=5x^2y^2*sqrt(x)}}} where every variable is positive.