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(√48 + √288 - √27) X (√800 - √300 - √72) =

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by sanju09 » Sat Sep 04, 2010 1:58 am
If (√48 + √288 - √27) × (√800 - √300 - √72) = a + b √6, then what is a + b equal to?
(A) 185
(B) 186
(C) 200
(D) 223
(E) 225



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by Rahul@gurome » Sat Sep 04, 2010 2:21 am
Solution:
sqrt(48) = 4*sqrt(3).
Sqrt(288) = 12*sqrt(2).
Sqrt(27) = 3*sqrt(3).
Sqrt(800) = 20*sqrt(2).
Sqrt(300) = 10*sqrt(3).
Sqrt(72) = 6*sqrt(2).

So the expression in the question is equal to [4*sqrt(3) + 12*sqrt(2) - 3*sqrt(3)] * [20*sqrt(2) - 10*sqrt(3) - 6*sqrt(2)] =
[sqrt(3) + 12*sqrt(2)] * [14*sqrt(2) - 10*sqrt(3)]
= 336 - 30 - 120*sqrt(6) + 14*sqrt(6)
= 306 - 106*sqrt(6).
So a = 306 and b = -106.
Or a+b = 306 - 106 = 200.
The correct answer is (C).
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