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1/(9-4√5)=?

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Math Revolution GMAT Instructor
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1/(9-4√5)=?  [#permalink]

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New post 29 May 2016, 20:56
2
1
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:04) correct 12% (00:51) wrong based on 66 sessions

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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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Re: 1/(9-4√5)=?  [#permalink]

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New post 29 May 2016, 21:11
1
This process is called rationalization of surds.

\(\frac{1}{(9-4√5)}\) can be multiplied in numerator and denominator by (9+4√5)

\(\frac{1*(9+4√5)}{(9-4√5)*(9+4√5)}\)

The denominator becomes \(9^2\) - \((4√5)^2\) = 81 - 80 = 1

Numerator is 9+4√5

A is the answer
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Re: 1/(9-4√5)=?  [#permalink]

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New post 30 May 2016, 07:46
MathRevolution 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.


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)
= 9 + 4√5
=

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

Cheers,
Brent
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Re: 1/(9-4√5)=?  [#permalink]

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New post 01 Jun 2016, 06:41
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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Re: 1/(9-4√5)=?  [#permalink]

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New post 08 Jun 2016, 14:04
FYI -- I received this exact question on the GMAT last weekend. I had a brainfart, wasted time, and got it wrong. Convinced it ruined my Quant split.
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Re: 1/(9-4√5)=?  [#permalink]

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New post 01 Jul 2017, 07:24
MathRevolution 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.


1/(9-4√5)

=\(\frac{1*(9 + 4√5)}{(9-4√5)(9 + 4√5)}\)

= \(\frac{9 + 4√5}{81 - 80}\)

= \(9+4√5\)

Thus, the answer must be (A) 9+4√5
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Re: 1/(9-4√5)=?   [#permalink] 01 Jul 2017, 07:24
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