Question 388546


{{{sqrt(12*x^7*w^10)}}} Start with the given expression.



{{{sqrt(4*3*x^7*w^10)}}} Factor {{{12}}} into {{{4*3}}}



{{{sqrt(4*3*x^2*x^2*x^2*x*w^10)}}} Factor {{{x^7}}} into {{{x^2*x^2*x^2*x}}}



{{{sqrt(4*3*x^2*x^2*x^2*x*w^2*w^2*w^2*w^2*w^2)}}} Factor {{{w^10}}} into {{{w^2*w^2*w^2*w^2*w^2}}}



{{{sqrt(4)*sqrt(3)*sqrt(x^2)*sqrt(x^2)*sqrt(x^2)*sqrt(x)*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)}}}.



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



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



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



{{{2w^5x^3*sqrt(3x)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(12*x^7*w^10)}}} simplifies to {{{2w^5x^3*sqrt(3x)}}}



In other words, {{{sqrt(12*x^7*w^10)=2w^5x^3*sqrt(3x)}}} where every variable is non-negative.