Question 368855


{{{sqrt(75*a^2*b)}}} Start with the given expression.



{{{sqrt(25*3*a^2*b)}}} Factor {{{75}}} into {{{25*3}}}



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



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



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



{{{5a*sqrt(3b)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(75*a^2*b)}}} simplifies to {{{5a*sqrt(3b)}}}



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



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