Question 547819


{{{sqrt(25*x^2*y^6*z)}}} Start with the given expression.



{{{sqrt(25*x^2*y^2*y^2*y^2*z)}}} Factor {{{y^6}}} into {{{y^2*y^2*y^2}}}



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



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



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



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



{{{5xy^3*sqrt(z)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(25*x^2*y^6*z)}}} simplifies to {{{5xy^3*sqrt(z)}}}



In other words, {{{sqrt(25*x^2*y^6*z)=5xy^3*sqrt(z)}}} where every variable is non-negative.