Closest approximation

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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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,
Brent

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