Question 1171178
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{{{sqrt(85+sqrt(2736)) = sqrt(a) + sqrt(b)}}}


{{{(sqrt(85+sqrt(2736)))^2 = (sqrt(a) + sqrt(b))^2}}} Squaring both sides


{{{85+sqrt(2736) = a + 2sqrt(ab)+ b}}}


{{{85+sqrt(4*684) = (a+b) + 2sqrt(ab)}}}


{{{85+sqrt(4)*sqrt(684) = (a+b) + 2sqrt(ab)}}} 


{{{85+2*sqrt(684) = (a+b) + 2sqrt(ab)}}}


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We see that the first pair of terms leads to a+b = 85, but we won't need this fact. 


Equating the second pair of terms leads to
{{{2*sqrt(684) = 2*sqrt(ab)}}}


{{{sqrt(684) = sqrt(ab)}}}


{{{(sqrt(684))^2 = (sqrt(ab))^2}}}


{{{684 = ab}}}


{{{ab = 684}}} which is the final answer.


Side note: You could use a+b = 85 and ab = 684 as a system of equations to solve for 'a' and b to find that a = 9 and b = 76; however, this isn't needed if you just want to find ab. 
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