Question 190644
{{{sqrt(3wy^3)*sqrt(12w^2y)}}} Start with the given expression.



{{{sqrt((3wy^3)(12w^2y))}}} Combine the roots using the identity {{{sqrt(A)*sqrt(B)=sqrt(A*B)}}}



{{{sqrt((3*12)(wy^3*w^2y))}}} Rearrange the terms.



{{{sqrt(36wy^3*w^2y)}}} Multiply 3 and 12 to get 36



{{{sqrt(36w^(1+2)y^(3+1))}}} Multiply the variable terms by adding the corresponding exponents.



{{{sqrt(36w^3y^4)}}} Add



{{{sqrt(36*w^2*w*y^4)}}} Factor {{{w^3}}} into {{{w^2*w}}}



{{{sqrt(36*w^2*w*y^2*y^2)}}} Factor {{{y^4}}} into {{{y^2*y^2}}}



{{{sqrt(36)*sqrt(w^2)*sqrt(w)*sqrt(y^2)*sqrt(y^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{6*sqrt(w^2)*sqrt(w)*sqrt(y^2)*sqrt(y^2)}}} Take the square root of {{{36}}} to get {{{6}}}.



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



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



{{{6wy^2*sqrt(w)}}} Rearrange and multiply.


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Answer:



So {{{sqrt(3wy^3)*sqrt(12w^2y)}}} simplifies to {{{6wy^2*sqrt(w)}}}



In other words, {{{sqrt(3wy^3)*sqrt(12w^2y)=6wy^2*sqrt(w)}}} where every variable is non-negative.