Question 194062

{{{sqrt(75*x^3*y^5)}}} Start with the given expression.



{{{sqrt(25*3*x^3*y^5)}}} Factor {{{75}}} into {{{25*3}}}



{{{sqrt(25*3*x^2*x*y^5)}}} Factor {{{x^3}}} into {{{x^2*x}}}



{{{sqrt(25*3*x^2*x*y^2*y^2*y)}}} Factor {{{y^5}}} into {{{y^2*y^2*y}}}



{{{sqrt(25)*sqrt(3)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y^2)*sqrt(y)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{5*sqrt(3)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{25}}} to get {{{5}}}.



{{{5*sqrt(3)*x*sqrt(x)*sqrt(y^2)*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{5*sqrt(3)*x*sqrt(x)*y*y*sqrt(y)}}} Take the square root of {{{y^2}}} to get {{{y}}}.



{{{5xy^2*sqrt(3xy)}}} Rearrange and combine the terms.


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Answer:



So {{{sqrt(75*x^3*y^5)}}} simplifies to {{{5xy^2*sqrt(3xy)}}}



In other words, {{{sqrt(75*x^3*y^5)=5xy^2*sqrt(3xy)}}} where every variable is non-negative.