Question 187304
{{{sqrt(64*x^3)}}} Start with the given expression.



{{{sqrt(64*x^2*x)}}} Factor {{{x^3}}} into {{{x^2*x}}}



{{{sqrt(64)*sqrt(x^2)*sqrt(x)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{8*sqrt(x^2)*sqrt(x)}}} Take the square root of {{{64}}} to get {{{8}}}.



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


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Answer:



So {{{sqrt(64*x^3)}}} simplifies to {{{8x*sqrt(x)}}}



In other words, {{{sqrt(64*x^3)=8x*sqrt(x)}}} where {{{x>=0}}}