Question 338323

{{{sqrt(64*d^6)}}} Start with the given expression.



{{{sqrt(64*d^2*d^2*d^2)}}} Factor {{{d^6}}} into {{{d^2*d^2*d^2}}}



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



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



{{{8*d*d*d}}} Take the square root of {{{d^2}}} to get {{{d}}}.



{{{8d^3}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(64*d^6)}}} simplifies to {{{8d^3}}}



In other words, {{{sqrt(64*d^6)=8d^3}}} where {{{d>=0}}}.



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