Question 309929


{{{sqrt(20*x^5*y)}}} Start with the given expression.



{{{sqrt(4*5*x^5*y)}}} Factor {{{20}}} into {{{4*5}}}



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



{{{sqrt(4)*sqrt(5)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{2*sqrt(5)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*sqrt(y)}}} Take the square root of {{{4}}} to get {{{2}}}.



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



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


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Answer:



So {{{sqrt(20*x^5*y)}}} simplifies to {{{2x^2*sqrt(5xy)}}}



In other words, {{{sqrt(20*x^5*y)=2x^2*sqrt(5xy)}}} where every variable is non-negative.