It is currently 22 Feb 2018, 04:16

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# S95-26

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43863

### Show Tags

16 Sep 2014, 00:50
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

57% (01:17) correct 43% (01:43) wrong based on 37 sessions

### HideShow timer Statistics

$$(\sqrt{7 + \sqrt{48}} + \sqrt{7 - \sqrt{48}})^2 =$$

A. $$1$$
B. $$7 - 4\sqrt{3}$$
C. $$14 - 4\sqrt{3}$$
D. $$14$$
E. $$16$$
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43863

### Show Tags

16 Sep 2014, 00:50
Official Solution:

$$(\sqrt{7 + \sqrt{48}} + \sqrt{7 - \sqrt{48}})^2 =$$

A. $$1$$
B. $$7 - 4\sqrt{3}$$
C. $$14 - 4\sqrt{3}$$
D. $$14$$
E. $$16$$

The question asks for the value of an expression. This expression is in the form of $$(x + y)^2$$, where

$$x = \sqrt{7 + \sqrt{48}}$$ and $$y = \sqrt{7 - \sqrt{48}}$$.

The expanded form of $$(x + y)^2$$ is $$x^2 + 2xy + y^2$$. If we substitute our values for $$x$$ and $$y$$, we get:

$$(\sqrt{7 + \sqrt{48}})^2 + 2(\sqrt{7 + \sqrt{48}})(\sqrt{7 - \sqrt{48}}) + (\sqrt{7 - \sqrt{48}})^2$$

We simplify, recalling that the product of two radical terms can be rewritten under one radical sign:

$$(7 + \sqrt{48}) + 2\leftarrow(\sqrt{(7 + \sqrt{48})(7 - \sqrt{48})}\rightarrow) + (7 - \sqrt{48})$$.

The middle term is the factored form of the difference of two squares, $$(x + y)(x - y) = x^2 - y^2$$. Simplify accordingly:

$$(7 + \sqrt{48}) + 2\leftarrow(\sqrt{(49 - 48)}\rightarrow) + (7 - \sqrt{48})$$

Simplify further, noting that the $$\sqrt{48}$$ terms cancel:

$$7 + 7 + 2\sqrt{1} = 14 + 2 = 16$$

_________________
Intern
Joined: 10 Jul 2017
Posts: 8

### Show Tags

31 Aug 2017, 06:18
Very good question
Re: S95-26   [#permalink] 31 Aug 2017, 06:18
Display posts from previous: Sort by

# S95-26

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.