Question 423941


{{{sqrt(12*x^8)}}} Start with the given expression.



{{{sqrt(4*3*x^8)}}} Factor {{{12}}} into {{{4*3}}}



{{{sqrt(4*3*x^2*x^2*x^2*x^2)}}} Factor {{{x^8}}} into {{{x^2*x^2*x^2*x^2}}}



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



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



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



{{{2x^4*sqrt(3)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(12*x^8)}}} simplifies to {{{2x^4*sqrt(3)}}}



In other words, {{{sqrt(12*x^8)=2x^4*sqrt(3)}}} where every variable is non-negative.



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