Question 554944


{{{sqrt(108*x^4)}}} Start with the given expression.



{{{sqrt(36*3*x^4)}}} Factor {{{108}}} into {{{36*3}}}



{{{sqrt(36*3*x^2*x^2)}}} Factor {{{x^4}}} into {{{x^2*x^2}}}



{{{sqrt(36)*sqrt(3)*sqrt(x^2)*sqrt(x^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{6*sqrt(3)*sqrt(x^2)*sqrt(x^2)}}} Take the square root of {{{36}}} to get {{{6}}}.



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



{{{6x^2*sqrt(3)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(108*x^4)}}} simplifies to {{{6x^2*sqrt(3)}}}



In other words, {{{sqrt(108*x^4)=6x^2*sqrt(3)}}} where x is non-negative.



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