GMAT Changed on April 16th - Read about the latest changes here

 It is currently 22 Apr 2018, 19:06

### 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

# (√27+√243)/√54=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5265
GMAT 1: 800 Q59 V59
GPA: 3.82

### Show Tags

01 Jun 2016, 06:47
Expert's post
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

75% (01:35) correct 25% (02:25) wrong based on 182 sessions

### HideShow timer Statistics

(√27+√243)/√54=?
A. 2√2
B. 2√3
C. 3√2
D. 3√3
E. √2

*An answer will be posted in 2 days.
[Reveal] Spoiler: OA

_________________

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 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" SVP Joined: 12 Sep 2015 Posts: 2298 Location: Canada (√27+√243)/√54=? [#permalink] ### Show Tags Updated on: 23 Nov 2016, 07:54 1 This post received KUDOS Expert's post Top Contributor 1 This post was BOOKMARKED MathRevolution wrote: (√27+√243)/√54=? A. 2√2 B. 2√3 C. 3√2 D. 3√3 E. √2 *An answer will be posted in 2 days. We'll use the following rule: √(xy) = (√x)(√y) √27 = √[(9)(3)] = (√9)(√3) = 3√3 √243 = √[(81)(3)] = (√81)(√3) = 9√3 √54 = √[(9)(6)] = (√9)(√6) = 3√6 So, (√27 + √243)/√54 = (3√3 + 9√3)/(3√6) = (12√3)/(3√6) = 4/√2 Check answer choices.... not there. Take 4/√2 and multiply top and bottom by √2. We get: (4/√2)(√2/√2) = (4√2)/(2) = 2√2 = A RELATED RESOURCES For more information on simplifying roots, watch these videos Cheers, Brent _________________ Brent Hanneson – Founder of gmatprepnow.com Originally posted by GMATPrepNow on 01 Jun 2016, 12:12. Last edited by GMATPrepNow on 23 Nov 2016, 07:54, edited 2 times in total. Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3396 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: (√27+√243)/√54=? [#permalink] ### Show Tags 01 Jun 2016, 12:15 1 This post was BOOKMARKED MathRevolution wrote: (√27+√243)/√54=? A. 2√2 B. 2√3 C. 3√2 D. 3√3 E. √2 *An answer will be posted in 2 days. $$\sqrt{27}$$ = $$3\sqrt{3}$$ $$\sqrt{243}$$ = $$9\sqrt{3}$$ $$\sqrt{54}$$ = $$3\sqrt{3}\sqrt{2}$$ $$\sqrt{27}$$ + $$\sqrt{243}$$ = $$3\sqrt{3}$$ + $$9\sqrt{3}$$ $$\sqrt{27}$$ + $$\sqrt{243}$$ = $$12\sqrt{3}$$ ( $$\sqrt{27}$$ + $$\sqrt{243}$$ ) / $$\sqrt{54}$$ = ( $$12\sqrt{3}$$ ) / ( $$3\sqrt{3}\sqrt{2}$$ ) $$3\sqrt{3}\sqrt{2}$$ = $$4/\sqrt{2}$$ = $$2\sqrt{2}$$ Hence answer will be (A) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5265 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: (√27+√243)/√54=? [#permalink] ### Show Tags 05 Jun 2016, 05:48 (√27+√243)/√54=(3√3+9√3)/3√6=12√3/3√6=4/√2=2√2. 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 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Joined: 28 Aug 2006
Posts: 303

### Show Tags

05 Jun 2016, 06:17
1
KUDOS
1
This post was
BOOKMARKED
Once you notice the following, figuring out the exact value of each of the given values can be eliminated and that should save some time

$$\frac{\sqrt{27} + \sqrt{243}}{\sqrt{54}} = \frac{ \sqrt{27} + ( \sqrt{27} \times \sqrt{9} ) } { \sqrt{27} \times \sqrt{2} } = \frac{ \sqrt{27} ( 1 + \sqrt{9} ) } { \sqrt{27} \times \sqrt{2} } = \frac{4}{\sqrt{2}} = 2\sqrt{2}$$
_________________
Intern
Joined: 13 May 2015
Posts: 18
Concentration: Finance, General Management
GMAT 1: 330 Q17 V12
GPA: 3.39

### Show Tags

24 Aug 2016, 20:57
I still don't see how 12√3)/(3√6) gives 2√2
Intern
Joined: 11 Jan 2016
Posts: 32

### Show Tags

23 Nov 2016, 07:33
cicerone wrote:
Once you notice the following, figuring out the exact value of each of the given values can be eliminated and that should save some time

$$\frac{\sqrt{27} + \sqrt{243}}{\sqrt{54}} = \frac{ \sqrt{27} + ( \sqrt{27} \times \sqrt{9} ) } { \sqrt{27} \times \sqrt{2} } = \frac{ \sqrt{27} ( 1 + \sqrt{9} ) } { \sqrt{27} \times \sqrt{2} } = \frac{4}{\sqrt{2}} = 2\sqrt{2}$$

Could you or somebody please explain how 4 divided by square root of 2 equals 2 times square root of 2? Not sure why but I don't get it.
Math Expert
Joined: 02 Sep 2009
Posts: 44599

### Show Tags

23 Nov 2016, 07:51
gracie90 wrote:
cicerone wrote:
Once you notice the following, figuring out the exact value of each of the given values can be eliminated and that should save some time

$$\frac{\sqrt{27} + \sqrt{243}}{\sqrt{54}} = \frac{ \sqrt{27} + ( \sqrt{27} \times \sqrt{9} ) } { \sqrt{27} \times \sqrt{2} } = \frac{ \sqrt{27} ( 1 + \sqrt{9} ) } { \sqrt{27} \times \sqrt{2} } = \frac{4}{\sqrt{2}} = 2\sqrt{2}$$

Could you or somebody please explain how 4 divided by square root of 2 equals 2 times square root of 2? Not sure why but I don't get it.

Multiply $$\frac{4}{\sqrt{2}}$$ by $$\frac{\sqrt{2}}{\sqrt{2}}$$ to get $$\frac{4}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}$$

This algebraic manipulation is called rationalization and is performed to eliminate irrational expression in the denominator.

Questions involving rationalization to practice:
if-x-0-then-106291.html
if-n-is-positive-which-of-the-following-is-equal-to-31236.html
in-the-diagram-not-drawn-to-scale-sector-pq-is-a-quarter-139282.html
in-the-diagram-what-is-the-value-of-x-129962.html
the-perimeter-of-a-right-isoscles-triangle-is-127049.html
which-of-the-following-is-equal-to-98531.html
if-x-is-positive-then-1-root-x-1-root-x-163491.html
1-2-sqrt3-64378.html
if-a-square-mirror-has-a-20-inch-diagonal-what-is-the-99359.html

Hope it helps.
_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2447
Location: United States (CA)

### Show Tags

08 Dec 2017, 11:34
MathRevolution wrote:
(√27+√243)/√54=?
A. 2√2
B. 2√3
C. 3√2
D. 3√3
E. √2

We are given (√27+√243)/√54. Let’s simplify each term.

√27 = √9 x √3 = 3√3

√243 = √81 x √3 = 9√3

√54 = √9 x √6 = 3√6

Thus:

(√27+√243)/√54 = (3√3 + 9√3)/(3√6) = (12√3)/(3√6) = 4/√2

Finally, we can rationalize 4/√2 by multiplying the numerator and denominator by √2 and we obtain:

(4/√2)(√2/√2) = (4√2)/2 = 2√2

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: (√27+√243)/√54=?   [#permalink] 08 Dec 2017, 11:34
Display posts from previous: Sort by