Question 336336

{{{sqrt(44*x^4*y^3)}}} Start with the given expression.



{{{sqrt(4*11*x^4*y^3)}}} Factor {{{44}}} into {{{4*11}}}



{{{sqrt(4*11*x^2*x^2*y^3)}}} Factor {{{x^4}}} into {{{x^2*x^2}}}



{{{sqrt(4*11*x^2*x^2*y^2*y)}}} Factor {{{y^3}}} into {{{y^2*y}}}



{{{sqrt(4)*sqrt(11)*sqrt(x^2)*sqrt(x^2)*sqrt(y^2)*sqrt(y)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{2*sqrt(11)*sqrt(x^2)*sqrt(x^2)*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{4}}} to get {{{2}}}.



{{{2*sqrt(11)*x*x*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{2*sqrt(11)*x*x*y*sqrt(y)}}} Take the square root of {{{y^2}}} to get {{{y}}}.



{{{2x^2y*sqrt(11y)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(44*x^4*y^3)}}} simplifies to {{{2x^2y*sqrt(11y)}}}



In other words, {{{sqrt(44*x^4*y^3)=2x^2y*sqrt(11y)}}} where every variable is non-negative.



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