<PRE><B>Question 1104114</B>
&lt;br&gt;
{{{(sqrt(a)+sqrt(b))^2 = a+b+2*sqrt(ab)}}}&lt;br&gt;
So if {{{sqrt(82+sqrt(3360)) = sqrt(a)+sqrt(b)}}}&lt;br&gt;
we must have&lt;br&gt;
{{{a+b=82}}} (1) and&lt;br&gt;
{{{2*sqrt(ab) = sqrt(3360)}}}
{{{sqrt(ab) = sqrt(840)}}}
{{{ab = 840}}} (2)&lt;br&gt;
Since the problem only asked us to find the product ab, we are done.&lt;br&gt;
We could go ahead and find the values of a and b by solving the pair of equations (1) and (2), using trial and error, or a graphing calculator, or algebra using either factoring or the quadratic formula; those values are 70 and 12.&lt;br&gt;
So while the problem didn&#39;t ask us to evaluate the square root,&lt;br&gt;
{{{sqrt(82+sqrt(3360)) = sqrt(12)+sqrt(70)}}}</PRE>