Question 295600


{{{sqrt(12*w^4)}}} Start with the given expression.



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



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



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



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



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



{{{2w^2*sqrt(3)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(12*w^4)}}} simplifies to {{{2w^2*sqrt(3)}}}



In other words, {{{sqrt(12*w^4)=2w^2*sqrt(3)}}} where {{{w>=0}}}