Question 375104


{{{sqrt(32*a^2*b)}}} Start with the given expression.



{{{sqrt(16*2*a^2*b)}}} Factor {{{32}}} into {{{16*2}}}



{{{sqrt(16)*sqrt(2)*sqrt(a^2)*sqrt(b)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{4*sqrt(2)*sqrt(a^2)*sqrt(b)}}} Take the square root of {{{16}}} to get {{{4}}}.



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



{{{4a*sqrt(2b)}}} Recombine the roots and rearrange the terms.


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Answer:



So {{{sqrt(32*a^2*b)}}} simplifies to {{{4a*sqrt(2b)}}}



In other words, {{{sqrt(32*a^2*b)=4a*sqrt(2b)}}} where every variable is non-negative.



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