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Closest approximation

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Closest approximation

by kaf » Tue Mar 10, 2009 1:51 am
Could someone kindly help in solving and explaining the solution to this question please

Of the following integers, which is the closest approximation to (√2 + √5)^2 ?

A. 7
B. 10
C. 13
D. 15
E. 17
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by sacx » Tue Mar 10, 2009 2:35 am
use (a+b)^2 = a^2 + b^2 +2ab
(√2 + √5)^2 = 2 + 5 + 2√10
~ 2 +5 + 2(3)
~ 13

√10 is slightly greater than 3, since 3^2 = 9
SACX
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by kaf » Tue Mar 10, 2009 2:54 am
thanks a lot
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by Turksonaaron » Sun Jun 25, 2017 6:20 am
Alternatively,
(√2 + √5)² by approximation
= (1.4 + 2')²
= (3.4')²
≈ 13
Hope it helps
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by Jay@ManhattanReview » Mon Jun 26, 2017 12:33 am
kaf wrote:Could someone kindly help in solving and explaining the solution to this question please

Of the following integers, which is the closest approximation to (√2 + √5)^2 ?

A. 7
B. 10
C. 13
D. 15
E. 17
(√2 + √5)^2 = 2 + 5 + 2√(2*5) = 7 + 2√(10)

7 + 2√(16) > 7 + 2√(10) > 7 + 2√(9)

15 > 7 + 2√(10) > 13

The value of 7 + 2√(10) lies between 13 and 15. Since √10 is relatively closer to √9 than to √16, the approximated value would be 13.

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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by Brent@GMATPrepNow » Mon Jun 26, 2017 5:59 am
I would have solved this using the same approach as the one Turksonaaron used.

For the GMAT, it's useful to memorize the 3 following approximations:

√2≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

Cheers,
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by Scott@TargetTestPrep » Fri Jun 30, 2017 8:16 am
kaf wrote:Could someone kindly help in solving and explaining the solution to this question please

Of the following integers, which is the closest approximation to (√2 + √5)^2 ?

A. 7
B. 10
C. 13
D. 15
E. 17
We can FOIL (√2 + √5)^2 as (√2 + √5)(√2 + √5):

(√2 + √5)(√2 + √5)

= (√2)^2 + 2(√2)(√5) + (√5)^2

= 2 + 2(√10) + 5

≈ 7 + 2(3)

= 13

Answer: C

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