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

 It is currently 02 Jun 2020, 10:53

### 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

# (5^(1/2) + 7^(1/2))^2 =

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64174

### Show Tags

15 May 2019, 21:46
00:00

Difficulty:

5% (low)

Question Stats:

82% (00:36) correct 18% (00:37) wrong based on 107 sessions

### HideShow timer Statistics

$$(\sqrt{5}+\sqrt{7})^2=$$

A. 12
B. $$12 + 2\sqrt{3}$$
C. $$12 + 4\sqrt{3}$$
D. $$12 + \sqrt{35}$$
E. $$12 + 2\sqrt{35}$$

_________________
CrackVerbal Representative
Joined: 12 May 2019
Posts: 68
Re: (5^(1/2) + 7^(1/2))^2 =  [#permalink]

### Show Tags

15 May 2019, 23:09
Formula to be used:

$$( a + b )^2 = a^2 + b^2 + 2ab$$

In this question, a = 5 and b = 7

$$(\sqrt{5} + \sqrt{7})^2$$ = $$(\sqrt{5})^2$$ + $$(\sqrt{7})^2$$ + 2 $$\sqrt{5}$$$$\sqrt{7}$$

= 5 + 7 + 2$$\sqrt{35}$$
= 12 + 2$$\sqrt{35}$$

_________________
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4886
GMAT 1: 770 Q49 V46
Re: (5^(1/2) + 7^(1/2))^2 =  [#permalink]

### Show Tags

16 May 2019, 05:11
1
Top Contributor
Bunuel wrote:
$$(\sqrt{5}+\sqrt{7})^2=$$

A. 12
B. $$12 + 2\sqrt{3}$$
C. $$12 + 4\sqrt{3}$$
D. $$12 + \sqrt{35}$$
E. $$12 + 2\sqrt{35}$$

Use FOIL to expand the product

Note: $$(\sqrt{x})(\sqrt{y})=\sqrt{xy}$$

So, $$(\sqrt{5}+\sqrt{7})^2=(\sqrt{5}+\sqrt{7})(\sqrt{5}+\sqrt{7})$$

$$=\sqrt{25}+\sqrt{35}+\sqrt{35}+\sqrt{49}$$

$$=5+2\sqrt{35}+7$$

$$=12+2\sqrt{35}$$

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10645
Location: United States (CA)
Re: (5^(1/2) + 7^(1/2))^2 =  [#permalink]

### Show Tags

19 May 2019, 18:32
Bunuel wrote:
$$(\sqrt{5}+\sqrt{7})^2=$$

A. 12
B. $$12 + 2\sqrt{3}$$
C. $$12 + 4\sqrt{3}$$
D. $$12 + \sqrt{35}$$
E. $$12 + 2\sqrt{35}$$

Since (x + y)^2 = x^2 + y^2 + 2xy, we have:

(√5)^2 + (√7)^2 + 2(√5)(√7)

5 + 7 + 2√35

12 + 2√35

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: (5^(1/2) + 7^(1/2))^2 =   [#permalink] 19 May 2019, 18:32