
It is currently Thu Apr 26, 2018 11:02 pm

View unanswered posts  View active topics

Page 1 of 1

[ 4 posts ] 

Author 
Message 
questioner

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.


Top 


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


Top 


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?


Top 


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


Top 



Page 1 of 1

[ 4 posts ] 

Who is online 
Users browsing this forum: No registered users and 2 guests 

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

