Question 615606


{{{sqrt(200*a^2*b)}}} Start with the given expression.



{{{sqrt(100*2*a^2*b)}}} Factor {{{200}}} into {{{100*2}}}



{{{sqrt(100)*sqrt(2)*sqrt(a^2)*sqrt(b)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{10*sqrt(2)*sqrt(a^2)*sqrt(b)}}} Take the square root of {{{100}}} to get {{{10}}}.



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



{{{10a*sqrt(2b)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(200*a^2*b)}}} simplifies to {{{10a*sqrt(2b)}}}



In other words, {{{sqrt(200*a^2*b)=10a*sqrt(2b)}}} where every variable is non-negative.