Question 253918


{{{sqrt(125*x^5*y^2*z^4)}}} Start with the given expression.



{{{sqrt(25*5*x^5*y^2*z^4)}}} Factor {{{125}}} into {{{25*5}}}



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



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



{{{sqrt(25)*sqrt(5)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(z^2)*sqrt(z^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



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



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



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



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



{{{5x^2yz^2*sqrt(5x)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(125*x^5*y^2*z^4)}}} simplifies to {{{5x^2yz^2*sqrt(5x)}}}



In other words, {{{sqrt(125*x^5*y^2*z^4)=5x^2yz^2*sqrt(5x)}}} where every variable is non-negative.