Question 303166


{{{sqrt(40*x^4*y^7)}}} Start with the given expression.



{{{sqrt(4*10*x^4*y^7)}}} Factor {{{40}}} into {{{4*10}}}



{{{sqrt(4*10*x^2*x^2*y^7)}}} Factor {{{x^4}}} into {{{x^2*x^2}}}



{{{sqrt(4*10*x^2*x^2*y^2*y^2*y^2*y)}}} Factor {{{y^7}}} into {{{y^2*y^2*y^2*y}}}



{{{sqrt(4)*sqrt(10)*sqrt(x^2)*sqrt(x^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{2*sqrt(10)*sqrt(x^2)*sqrt(x^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{4}}} to get {{{2}}}.



{{{2*sqrt(10)*x*x*sqrt(y^2)*sqrt(y^2)*sqrt(y^2)*sqrt(y)}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{2*sqrt(10)*x*x*y*y*y*sqrt(y)}}} Take the square root of {{{y^2}}} to get {{{y}}}.



{{{2x^2y^3*sqrt(10y)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(40*x^4*y^7)}}} simplifies to {{{2x^2y^3*sqrt(10y)}}}



In other words, {{{sqrt(40*x^4*y^7)=2x^2y^3*sqrt(10y)}}} where every variable is non-negative.