Question 375118


{{{sqrt(27*a^3)}}} Start with the given expression.



{{{sqrt(9*3*a^3)}}} Factor {{{27}}} into {{{9*3}}}



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



{{{sqrt(9)*sqrt(3)*sqrt(a^2)*sqrt(a)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



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



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



{{{3a*sqrt(3a)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(27*a^3)}}} simplifies to {{{3a*sqrt(3a)}}}



In other words, {{{sqrt(27*a^3)=3a*sqrt(3a)}}} where every variable is non-negative.



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