Target Test Prep 20% Off Flash Sale is on! Code: FLASH20

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

Closest approximation

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 53
Joined: Mon Feb 09, 2009 12:18 am
Thanked: 1 times

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
Top
Master | Next Rank: 500 Posts
Posts: 139
Joined: Wed Oct 22, 2008 4:36 am
Thanked: 17 times

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
Top
Senior | Next Rank: 100 Posts
Posts: 53
Joined: Mon Feb 09, 2009 12:18 am
Thanked: 1 times

by kaf » Tue Mar 10, 2009 2:54 am
thanks a lot
Top
Junior | Next Rank: 30 Posts
Posts: 14
Joined: Thu Mar 23, 2017 10:58 pm
GMAT Score:470

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
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

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
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7247
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1