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by avenus » Mon May 04, 2009 9:52 am
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by PussInBoots » Mon May 04, 2009 12:33 pm
The answer is D.

Square the whole equation => simplify => take a square root

Here are some hints you'll need to use at some point:
(a+b) (a-b) = a^2 - b^2
24^2 - 5^2 * 23 = 24^2 - 25 * 23 = 24^2 - (24+1) * (24 - 1)
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by Ian Stewart » Mon May 04, 2009 1:02 pm
PussInBoots has a great solution above, and it's particularly useful to notice that you can compute 24^2 - 25*23 quickly using the difference of squares. Considering the answer choices here, however, if you notice that 5*sqrt(23) is almost equal to 24, then sqrt(24 - 5*sqrt(23)) must be very close to zero, while sqrt(24 + 5*sqrt(23)) must be very close in value to sqrt(48) ~ 7. So we're looking for an answer that is approximately equal to 7, and there's only one answer choice that's even remotely close.
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