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Post subject: GMAT Arithmetic Posted: Tue Aug 17, 2010 11:26 am 

Joined: Sun May 30, 2010 3:15 am Posts: 424

(√54 – √6) / (√54 + √6) = A. 1/3 B. √6/6 C. 1/2 D. 5/8 E. 1
(C) √54 = √(9 × 6) = 3√6.
So (√54 – √6) / (√54 + √6) = (3√6 – √6) / (3√6 + √6) = (2√6) / (4 √6) = 1/2.
The correct answer is C.
ALTERNATIVE SOLUTION: When we see expression in denominator that includes radicals the first method to simplify it is to use formula a² – b² = (a + b)(a – b). We see that in this case we have only (a + b) in the denominator. So let us multiply both numerator and denominator by (√54 – √6): [(√54 – √6) × (√54 – √6)] / [(√54 + √6) × (√54 – √6)] = = (√54 – √6)² / (54 – 6) = (54 + 6 – 2 × 18) / 48 = 24 / 48 = 1/2 The answer is choice (C).
 Hello. I do not understand how the numerator breaks out into (54 + 6 – 2 × 18). Please explain. Thank you.


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Gennadiy

Post subject: Re: math (test 1, question 8): fractions, irrationality Posted: Tue Aug 17, 2010 11:30 am 

Joined: Sun May 30, 2010 2:23 am Posts: 498

When we multiply both numerator and denominator by (√54 – √6) numerator becomes: (√54 – √6) × (√54 – √6) = (√54 – √6)² = = (√54)² + (√6)² – 2 × √54 × √6 = = 54 + 6 – 2 × √(54 × 6) = 54 + 6 – 2 × 18 = 24


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questioner

Post subject: Re: math (test 1, question 8): fractions, irrationality Posted: Tue Nov 02, 2010 1:45 am 

Joined: Sun May 30, 2010 3:15 am Posts: 424

Where did the 18 come from please?


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Gennadiy

Post subject: Re: math (test 1, question 8): fractions, irrationality Posted: Tue Nov 02, 2010 1:51 am 

Joined: Sun May 30, 2010 2:23 am Posts: 498

18 is √(54 × 6)
√(54 × 6) = √(2 × 3 × 3 × 3 × 2 × 3) = √(2 × 3 × 3)² = √(18²) = 18


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