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Which is greater \sqrt of 8 or the length of line segment PR

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Carcass
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Which is greater \sqrt of 8 or the length of line segment PR [#permalink] New post   19 Jan 2020, 12:33
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Quantity A
Quantity B
\(\sqrt{8}\)
The length of line segment PR



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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theBrahmaTiger
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Re: Which is greater \sqrt of 8 or the length of line segment PR [#permalink] New post   20 Jan 2020, 08:44
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Carcass wrote:
Attachment:
#greprepclub the length of line segment PR.jpg


Quantity A
Quantity B
\(\sqrt{8}\)
The length of line segment PR



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Kudos for the right answer and explanation


Triangle QSR is a 45-45-90 triangle, so by Pythagoras theorem,

SR is = √2

PQS is a 30-60-90 triangle, which should divide the sides in 1:√3:2 ratio

so for this triangle, the sides become √2:√6:2√2

PS = √6

Quantity B: PR = √6 + √2

Quantity A = √8 = 2√2 = √2+√2

√6 > √2

Hence, Quantity B is greater.
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Re: Which is greater \sqrt of 8 or the length of line segment PR [#permalink] New post   08 Sep 2022, 01:28
Hello from the GRE Prep Club BumpBot!

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Re: Which is greater \sqrt of 8 or the length of line segment PR [#permalink]
08 Sep 2022, 01:28
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