Question 628188


{{{sqrt(567*w^12)}}} Start with the given expression.



{{{sqrt(81*7*w^12)}}} Factor {{{567}}} into {{{81*7}}}



{{{sqrt(81*7*w^2*w^2*w^2*w^2*w^2*w^2)}}} Factor {{{w^12}}} into {{{w^2*w^2*w^2*w^2*w^2*w^2}}}



{{{sqrt(81)*sqrt(7)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{9*sqrt(7)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)*sqrt(w^2)}}} Take the square root of {{{81}}} to get {{{9}}}.



{{{9*sqrt(7)*w*w*w*w*w*w}}} Take the square root of {{{w^2}}} to get {{{w}}}.



{{{9w^6*sqrt(7)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(567*w^12)}}} simplifies to {{{9w^6*sqrt(7)}}}



In other words, {{{sqrt(567*w^12)=9w^6*sqrt(7)}}} where 'w' is non-negative.


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