Question 761663

{{{sqrt(18*x^3*y^2)}}} Start with the given expression.



{{{sqrt(9*2*x^3*y^2)}}} Factor {{{18}}} into {{{9*2}}}



{{{sqrt(9*2*x^2*x*y^2)}}} Factor {{{x^3}}} into {{{x^2*x}}}



{{{sqrt(9)*sqrt(2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{3*sqrt(2)*sqrt(x^2)*sqrt(x)*sqrt(y^2)}}} Take the square root of {{{9}}} to get {{{3}}}.



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



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



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



{{{3*abs(x*y)*sqrt(2x)}}} Combine the absolute values.


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Answer:



So {{{sqrt(18*x^3*y^2)}}} simplifies to {{{3*abs(x*y)*sqrt(2x)}}}



In other words, {{{sqrt(18*x^3*y^2)=3*abs(x*y)*sqrt(2x)}}}