Question 1104114
.
This problem was formulated INCORRECTLY.


The correct formulation is THIS:


<pre>
    The radical {{{ sqrt (82 + sqrt (3360)) }}} can be expressed as {{{sqrt (a) + sqrt (b)}}}, where a < b <U>are positive integer numbers</U>. 
    What is the product ab?
</pre>

Then the solution by @greenestamps is correct.


Otherwise, without the requirement that "a" and "b" are integer, the problem has INFINITELY MANY solutions.