SOLUTION: The radical {{{ sqrt (82 + sqrt (3360)) }}} can be expressed as {{{ sqrt (a) + sqrt (b) }}}, where a < b. What is the product ab?

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Question 1104114: The radical can be expressed as , where a < b. What is the product ab?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!




So if

we must have

(1) and



(2)

Since the problem only asked us to find the product ab, we are done.

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.

So while the problem didn't ask us to evaluate the square root,
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
This problem was formulated INCORRECTLY.

The correct formulation is THIS: 

    The radical  can be expressed as , where a < b are positive integer numbers. 
    What is the product ab?

Then the solution by @greenestamps is correct.

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



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