Question 555508


{{{sqrt(216*x^3)}}} Start with the given expression.



{{{sqrt(36*6*x^3)}}} Factor {{{216}}} into {{{36*6}}}



{{{sqrt(36*6*x^2*x)}}} Factor {{{x^3}}} into {{{x^2*x}}}



{{{sqrt(36)*sqrt(6)*sqrt(x^2)*sqrt(x)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



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



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



{{{6x*sqrt(6x)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(216*x^3)}}} simplifies to {{{6x*sqrt(6x)}}}



In other words, {{{sqrt(216*x^3)=6x*sqrt(6x)}}} where every variable is non-negative.


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