Question 188724
{{{(2*sqrt(5xy))(2*sqrt(10x^2y^3))}}} Start with the given expression.



{{{(2*2)*(sqrt(5xy)*sqrt(10x^2y^3))}}} Rearrange the terms.



{{{4*(sqrt(5xy)*sqrt(10x^2y^3))}}} Multiply 2 and 2 to get 4



{{{4*sqrt((5xy)(10x^2y^3))}}} Combine the roots using the identity {{{sqrt(x)*sqrt(y)=sqrt(x*y)}}}



{{{4*sqrt((5*10)(xy*x^2y^3))}}} Rearrange the terms inside the root.



{{{4*sqrt(50xy*x^2y^3)}}} Multiply 5 and 10 to get 50



{{{4*sqrt(50x^(1+2)y^(1+3))}}} Multiply the variable terms by adding the exponents.



{{{4*sqrt(50x^3y^4)}}} Add



{{{4*sqrt(25*2*x^3*y^4)}}} Factor {{{50}}} into {{{25*2}}}



{{{4*sqrt(25*2*x^2*x*y^4)}}} Factor {{{x^3}}} into {{{x^2*x}}}



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



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



{{{4*5*sqrt(2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y^2)}}} Take the square root of {{{25}}} to get {{{5}}}.



{{{20*sqrt(2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)*sqrt(y^2)}}} Multiply 4 and 5 to get 20



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



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



{{{20xy^2*sqrt(2x)}}} Rearrange and multiply the terms.


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Answer:



So {{{(2*sqrt(5xy))(2*sqrt(10x^2y^3))}}} simplifies to {{{20xy^2*sqrt(2x)}}}



In other words, {{{(2*sqrt(5xy))(2*sqrt(10x^2y^3))=20xy^2*sqrt(2x)}}} where every variable is non-negative.