Question 190643


{{{sqrt(48*x^3*y^2)}}} Start with the given expression.



{{{sqrt(16*3*x^3*y^2)}}} Factor {{{48}}} into {{{16*3}}}



{{{sqrt(16*3*x^2*x*y^2)}}} Factor {{{x^3}}} into {{{x^2*x}}}



{{{sqrt(16)*sqrt(3)*sqrt(x^2)*sqrt(x)*sqrt(y^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{4*sqrt(3)*sqrt(x^2)*sqrt(x)*sqrt(y^2)}}} Take the square root of {{{16}}} to get {{{4}}}.



{{{4*sqrt(3)*x*sqrt(x)*sqrt(y^2)}}} Take the square root of {{{x^2}}} to get {{{x}}}.



{{{4*sqrt(3)*x*sqrt(x)*y}}} Take the square root of {{{y^2}}} to get {{{y}}}.



{{{4xy*sqrt(3x)}}} Rearrange and combine the terms.


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Answer:



So {{{sqrt(48*x^3*y^2)}}} simplifies to {{{4xy*sqrt(3x)}}}



In other words, {{{sqrt(48*x^3*y^2)=4xy*sqrt(3x)}}} where every variable is non-negative.