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GRE Math Challenge #66- Square Root of 2

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GRE Math Challenge #66- Square Root of 2 [#permalink] New post 03 May 2015, 00:56
Expert's post
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Question Stats:

71% (00:25) correct 28% (00:31) wrong based on 7 sessions
Quantity A: \((1 + \sqrt{2})^2\)
Quantity B: 3

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #66- Square Root of 2 [#permalink] New post 24 Sep 2017, 14:57
Expert's post
sandy wrote:
Quantity A: \((1 + \sqrt{2})^2\)
Quantity B: 3



There are a few ways to handle this question.

One is to use some approximation.

On test day, it's a good idea to know the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, we get something like this:
Quantity A: (1 + 1.4)²
Quantity B: 3

Simplify:
Quantity A: (2.4)²
Quantity B: 3

ASIDE: if √5 ≈ 2.2, then we know that (2.2)² ≈ 5
So, (2.4)² = a number that's bigger than 5

So, we have:
Quantity A: a number that's bigger than 5
Quantity B: 3

Answer: A

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: GRE Math Challenge #66- Square Root of 2 [#permalink] New post 24 Sep 2017, 15:01
Expert's post
sandy wrote:
Quantity A: \((1 + \sqrt{2})^2\)
Quantity B: 3


Another approach is to use the FOIL method and matching operations

Given:
Quantity A: (1 + √2)²
Quantity B: 3

Use the FOIL method to expand Quantity A:
Quantity A: 1 + √2 + √2 + 2
Quantity B: 3

Simplify:
Quantity A: 3 + 2√2
Quantity B: 3

Subtract 3 from both sides:
Quantity A: 2√2
Quantity B: 0

Quantity A is clearly bigger than Quantity B

Answer: A

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Re: GRE Math Challenge #66- Square Root of 2   [#permalink] 24 Sep 2017, 15:01
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GRE Math Challenge #66- Square Root of 2

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