Question 376607


{{{sqrt(75*s^5*t^10)}}} Start with the given expression.



{{{sqrt(25*3*s^5*t^10)}}} Factor {{{75}}} into {{{25*3}}}



{{{sqrt(25*3*s^2*s^2*s*t^10)}}} Factor {{{s^5}}} into {{{s^2*s^2*s}}}



{{{sqrt(25*3*s^2*s^2*s*t^2*t^2*t^2*t^2*t^2)}}} Factor {{{t^10}}} into {{{t^2*t^2*t^2*t^2*t^2}}}



{{{sqrt(25)*sqrt(3)*sqrt(s^2)*sqrt(s^2)*sqrt(s)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{5*sqrt(3)*sqrt(s^2)*sqrt(s^2)*sqrt(s)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)}}} Take the square root of {{{25}}} to get {{{5}}}.



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



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



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


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Answer:



So {{{sqrt(75*s^5*t^10)}}} simplifies to {{{5s^2t^5*sqrt(3s)}}}



In other words, {{{sqrt(75*s^5*t^10)=5s^2t^5*sqrt(3s)}}} where every variable is non-negative.



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