GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 Jan 2020, 01:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# (1+√3+√5)^2-(√3+√5)^2=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

26 Jun 2016, 07:38
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:42) correct 21% (02:05) wrong based on 219 sessions

### HideShow timer Statistics

(1+√3+√5)^2-(√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

*An answer will be posted in 2 days.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4226

### Show Tags

Updated on: 16 Oct 2018, 07:54
4
Top Contributor
2
(1+√3+√5)² - (√3+√5)² = ?

A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

Nice question!
First recognize that (1+√3+√5)² - (√3+√5)² is a DIFFERENCE OF SQUARES.
Here are some examples of differences of squares:
x² - 25y²
4x² - 9y²
49m² - 100k²

In general, we can factor differences of squares as follows:
- = (a+b)(a-b)

So, (1+√3+√5)² - (√3+√5)² = [(1+√3+√5) + (√3+√5)][(1+√3+√5) - (√3+√5)]
= [1+2√3+2√5][1]
= 1+2√3+2√5

_________________
Test confidently with gmatprepnow.com

Originally posted by GMATPrepNow on 26 Jun 2016, 12:42.
Last edited by GMATPrepNow on 16 Oct 2018, 07:54, edited 1 time in total.
##### General Discussion
Current Student
Joined: 18 Oct 2014
Posts: 791
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98

### Show Tags

26 Jun 2016, 08:27
3
(1+√3+√5)^2-(√3+√5)^2

(1+√3)^2 + 5 +2 (1+√3) (√5) - ( 3 +5 + 2√3√5)

1+ 3+ 2√3 +5 +2 √5 + 2 √15 - 3-5 -2√15

1+2√3+2√5

_________________
I welcome critical analysis of my post!! That will help me reach 700+
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82

### Show Tags

27 Jun 2016, 18:30
A^2-B^2=(A+B)(A-B). Hence, the correct answer is A.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 01 Jan 2016
Posts: 52
GPA: 3.75
WE: Engineering (Energy and Utilities)

### Show Tags

20 Aug 2017, 05:09
MathRevolution wrote:
(1+√3+√5)^2-(√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

*An answer will be posted in 2 days.

you can even do it with (A+B)^2 formula:

let √3+√5=x
Then the question becomes:
(1+x)^2-(x)^2=1^2+x^2+2x-x^2=1+2x=1+2(√3+√5)= option B
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4226

### Show Tags

20 Aug 2017, 06:27
1
Top Contributor
MathRevolution wrote:
(1+√3+√5)^2 - (√3+√5)^2=?
A. 1+2√3+2√5
B. 1+2√3+3√5
C. 1-√3+√5
D. 1+√3-√5
E. √3+√5

Another approach:

For test day, everyone should know the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, (1+√3+√5)² - (√3+√5)² ≈ (1+ 1.7 + 2.2)² - (1.7 + 2.2)²
≈ (4.9)² - (3.9)²
≈ 25 - 16
9

A. 1+2√3+2√5 ≈ 1 + 2(1.7) + 2(2.2) ≈ 8.8. CLOSE - KEEP
B. 1+2√3+3√5 ≈ 1 + 2(1.7) + 3(2.2) ≈ 11. ELIMINATE
C. 1-√3+√5 ≈ 1 - 1.7 + 2.2 ≈ 1.5. ELIMINATE
D. 1+√3-√5 ≈1 + 1.7 - 2.2 ≈ 0.4. ELIMINATE
E. √3+√5 ≈ 1.7 + 2.2 ≈ 3.9. ELIMINATE

_________________
Test confidently with gmatprepnow.com
Non-Human User
Joined: 09 Sep 2013
Posts: 14013

### Show Tags

08 Dec 2019, 09:31
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: (1+√3+√5)^2-(√3+√5)^2=?   [#permalink] 08 Dec 2019, 09:31
Display posts from previous: Sort by