Question 639181


{{{sqrt(25*x^5)}}} Start with the given expression.



{{{sqrt(25*x^2*x^2*x)}}} Factor {{{x^5}}} into {{{x^2*x^2*x}}}



{{{sqrt(25)*sqrt(x^2)*sqrt(x^2)*sqrt(x)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{5*sqrt(x^2)*sqrt(x^2)*sqrt(x)}}} Take the square root of {{{25}}} to get {{{5}}}.



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



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


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Answer:



So {{{sqrt(25*x^5)}}} simplifies to {{{5x^2*sqrt(x)}}}



In other words, {{{sqrt(25*x^5)=5x^2*sqrt(x)}}} where x is non-negative.