Question 531015


{{{sqrt(176*a^3*b^5)}}} Start with the given expression.



{{{sqrt(16*11*a^3*b^5)}}} Factor {{{176}}} into {{{16*11}}}



{{{sqrt(16*11*a^2*a*b^5)}}} Factor {{{a^3}}} into {{{a^2*a}}}



{{{sqrt(16*11*a^2*a*b^2*b^2*b)}}} Factor {{{b^5}}} into {{{b^2*b^2*b}}}



{{{sqrt(16)*sqrt(11)*sqrt(a^2)*sqrt(a)*sqrt(b^2)*sqrt(b^2)*sqrt(b)}}} Break up the square root using the identity {{{sqrt(A*B)=sqrt(A)*sqrt(B)}}}.



{{{4*sqrt(11)*sqrt(a^2)*sqrt(a)*sqrt(b^2)*sqrt(b^2)*sqrt(b)}}} Take the square root of {{{16}}} to get {{{4}}}.



{{{4*sqrt(11)*a*sqrt(a)*sqrt(b^2)*sqrt(b^2)*sqrt(b)}}} Take the square root of {{{a^2}}} to get {{{a}}}.



{{{4*sqrt(11)*a*sqrt(a)*b*b*sqrt(b)}}} Take the square root of {{{b^2}}} to get {{{b}}}.



{{{4ab^2*sqrt(11ab)}}} Rearrange and multiply the terms.


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Answer:



So {{{sqrt(176*a^3*b^5)}}} simplifies to {{{4ab^2*sqrt(11ab)}}}



In other words, {{{sqrt(176*a^3*b^5)=4ab^2*sqrt(11ab)}}} where every variable is non-negative.