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Equal to [1/(srt3-srt2)]^2

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by das.ashmita » Thu Jul 12, 2012 12:30 am
let a = 1/(sqrt 3 - sqrt 2)

Multiply and divide the num and denom by (sqrt 3 + sqrt 2)

=> (sqrt 3 + sqrt 2) / [(sqrt 3 + sqrt 2)(sqrt 3 - sqrt 2)]

Since (x+y)(x-y) = x^2 - y^2
therefore, (sqrt 3 + sqrt2) / (3-2) = (sqrt 3 + sqrt2)

Now a^2 = (sqrt 3 + sqrt 2)^2
= 3+2+2(sqrt 3)(sqrt 2 ) = 5 + 2(sqrt 6)

Hope it helps :)
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by GMATGuruNY » Thu Jul 12, 2012 3:02 am
alex.gellatly wrote:Which of the following is equal to [1/(srt3-srt2)]^2?

1
5
srt6
5-srt6
5+2srt6
Ballpark.

[1/(√3-√2)]²
≈ [1/(1.7-1.4)]²
= (1/.3)²
= (10/3)²
= 100/9
≈ 10.

Only answer choice E is viable; the other answer choices are clearly too small.

The correct answer is E.
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