Question 200951

{{{sqrt(12*c^6)}}} Start with the given expression.



{{{sqrt(4*3*c^6)}}} Factor {{{12}}} into {{{4*3}}}



{{{sqrt(4*3*c^2*c^2*c^2)}}} Factor {{{c^6}}} into {{{c^2*c^2*c^2}}}



{{{sqrt(4)*sqrt(3)*sqrt(c^2)*sqrt(c^2)*sqrt(c^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{2*sqrt(3)*sqrt(c^2)*sqrt(c^2)*sqrt(c^2)}}} Take the square root of {{{4}}} to get {{{2}}}.



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



{{{2c^3*sqrt(3)}}} Rearrange and combine the terms.


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Answer:



So {{{sqrt(12*c^6)}}} simplifies to {{{2c^3*sqrt(3)}}}



In other words, {{{sqrt(12*c^6)=2c^3*sqrt(3)}}} where {{{c>=0}}}.