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What is the value of 2/(2- 2)?
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28 Jul 2022, 22:28
28 Jul 2022, 22:28
Expert Reply
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Question Stats:
72% (00:44) correct
27% (02:05) wrong based on 11 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
(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the value of 2/(2- 2)?
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30 Jul 2022, 07:15
30 Jul 2022, 07:15
1
Carcass wrote:
What is the value of \(\frac{2}{2- \sqrt{2}}\)?
(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4
(A) 1
(B) 2
(C) 1 + √2
(D) 2 + √2
(E) 4
APPROACH #1: Use conjugate
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
APPROACH #2: Use calculator
Evaluate \(\frac{2}{2- \sqrt{2}}\) to get 3.414
Then evaluate each answer choice until you get 3.414
Answer: D
gmatclubot
Re: What is the value of 2/(2- 2)? [#permalink]
30 Jul 2022, 07:15
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