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What is the value of 2/(2- √2)?

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Bunuel
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What is the value of 2/(2- √2)? [#permalink] What is the value of 2/(2- √2)?   25 Apr 2017, 03:30
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A
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C
D
E

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82% (00:54) correct 18% (01:10) wrong based on 448 sessions
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What is the value of \(\frac{2}{2- \sqrt{2}}\)?

(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4
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D
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BrentGMATPrepNow
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What is the value of 2/(2- 2)? [#permalink] What is the value of 2/(2- √2)?   Updated on: 30 Jul 2022, 08:12
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Bunuel
What is the value of \(\frac{2}{2- \sqrt{2}}\)?

(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4

Given: 2/(2 - √2)

Our goal is to rationalize ("fix") the denominator so that it doesn't have a root.
We'll do this by multiplying the numerator and denominator by the conjugate of 2 - √2, which is 2 + √2

Numerator: 2(2 + √2) = 4 + 2√2
Denominator: (2 - √2)(2 + √2) = 4 - 2 = 2

So, 2/(2 - √2) = (4 + 2√2)/2 = 2 + √2

Answer: D

Originally posted by BrentGMATPrepNow on 25 Apr 2017, 06:11.
Last edited by BrentGMATPrepNow on 30 Jul 2022, 08:12, edited 1 time in total.
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Re: What is the value of 2/(2- √2)? [#permalink] What is the value of 2/(2- √2)?   28 Apr 2017, 15:06
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Bunuel
What is the value of \(\frac{2}{2- \sqrt{2}}\)?

(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4

We must rationalize the denominator by multiplying the entire expression by (2 +√2)/(2 +√2). Let’s simplify the given equation:

2/(2 - √2) x (2 + √2)/(2 + √2) = (4 + 2√2)/[2^2 - (√2)^2] = (4 + 2√2)/(4 - 2) = (4 + 2√2)/2 = 2 + √2

Answer: D
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BrentGMATPrepNow
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What is the value of 2/(2- 2)? [#permalink] What is the value of 2/(2- √2)?   Updated on: 30 Jul 2022, 08:17
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Bunuel
What is the value of \(\frac{2}{2- \sqrt{2}}\)?

(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4

Another approach:

All GMAT test-takers should all memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, 2/(2 - √2) ≈ 2/(2 - 1.4)
≈ 2/(0.6)
≈ 3.3

Now check the answer choices...
(A) 1 nope (ELIMINATE)
(B) 2 nope (ELIMINATE)
(C) 1 + √2 ≈ 1 + 1.4 ≈ 2.4 nope (ELIMINATE)
(D) 2 + √2 ≈ 2 + 1.4 ≈ 3.4 looks good. KEEP
(E) 4 nope (ELIMINATE)

Answer:
Show Spoiler
D

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 25 Apr 2017, 06:17.
Last edited by BrentGMATPrepNow on 30 Jul 2022, 08:17, edited 1 time in total.
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Re: What is the value of 2/(2- 2)? [#permalink] What is the value of 2/(2- √2)?   06 Oct 2023, 03:27
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Re: What is the value of 2/(2- 2)? [#permalink]
06 Oct 2023, 03:27