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1/(9-4√5)=?

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1/(9-4√5)=?

by Max@Math Revolution » Sun May 29, 2016 7:57 pm
1/(9-4√5)=?
A. 9+4√5
B. 9-4√5
C. 9+2√5
D. 9-2√5
E. 4+9√5

*An answer will be posted in 2 days.
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by shwetagoyal121 » Mon May 30, 2016 2:24 am
Max@Math Revolution wrote:1/(9-4√5)=?
A. 9+4√5
B. 9-4√5
C. 9+2√5
D. 9-2√5
E. 4+9√5

*An answer will be posted in 2 days.
Answer: A (Method: rationalize)
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by Brent@GMATPrepNow » Mon May 30, 2016 6:44 am
Max@Math Revolution wrote:1/(9-4√5)=?
A. 9+4√5
B. 9-4√5
C. 9+2√5
D. 9-2√5
E. 4+9√5
This question requires us to rationalize ("fix") the denominator.
For more on this technique, see https://www.gmatprepnow.com/module/gmat ... video/1044

Given: 1/(9-4√5)
Multiply top and bottom by the CONJUGATE of 9-4√5, which is 9+4√5
So, 1/(9-4√5) = (1)(9+4√5)/(9-4√5)(9+4√5)
= (9 + 4√5)/(81 + 36√5 - 36√5 - 80)
= (9 + 4√5)/(1)
= [spoiler]9 + 4√5[/spoiler]
= A

For more information on multiplying roots, see https://www.gmatprepnow.com/module/gmat ... video/1039

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Wed Jun 01, 2016 5:40 am
1/(9-4√5)=(9+4√5)/(9-4√5)(9+4√5)=(9+4√5)/(81-80)=(9+4√5). Hence, the correct answer is A.
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