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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

by dunkin77 » Sun Jun 17, 2007 8:42 am

Which of the following is equal to [1/(√3-√2)]^2?

A. 1
B. 5
C. √6
D. 5 - √6
E. 5 + 2√6

Hi,

my answer was 5 + 2√6 / -19 .... not even in the choice. can anyone help?

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Source: Beat The GMAT — Problem Solving | Sun Jun 17, 2007 8:42 am

RM: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Sat Jun 16, 2007 10:58 pm

by RM » Sun Jun 17, 2007 10:33 am

[1/(√3-√2)]^2

To rationalize, multiply numerator and denominator with (√3+√2).
Denominator will equal 1, (√3-√2) * (√3+√2), Formula used [(a+b)*(a-b) = a2 - b2]
Numerator will equal (√3+√2)

[1/(√3-√2)]^2 = [(√3+√2)/1] ^2

Or, = 3 + 2 + 2*√3*√2 = 5 + 2√6,

Choice E.

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