Last visit was: 22 Apr 2026, 22:54 It is currently 22 Apr 2026, 22:54
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
555-605 (Medium)|   Algebra|   Roots|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,763
Own Kudos:
810,698
 [26]
Given Kudos: 105,850
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,763
Kudos: 810,698
 [26]
(180^(1/2) +45^(1/2))/135^(1/2) 25 Apr 2017, 03:08
Kudos
Add Kudos
26
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

35% (medium)

Question Stats:

77% (02:05) correct 23% (02:50) wrong based on 811 sessions

History

Date
Time
Result
Not Attempted Yet
\(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\)

A. \(\sqrt{3}\)

B. \(3\sqrt{3}\)

C. \(5\sqrt{3}\)

D. \(3\sqrt{5}\)

E. \(5\sqrt{5}\)
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,447
 [7]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,447
 [7]
(180^(1/2) +45^(1/2))/135^(1/2) Updated on: 08 Feb 2021, 09:13
Originally posted by BrentGMATPrepNow on 25 Apr 2017, 06:26.
Last edited by BrentGMATPrepNow on 08 Feb 2021, 09:13, edited 2 times in total.
3
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
Bunuel
\(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\)

A. \(\sqrt{3}\)

B. \(3\sqrt{3}\)

C. \(5\sqrt{3}\)

D. \(3\sqrt{5}\)

E. \(5\sqrt{5}\)
Show more

We'll simplify each root by using the rule: √(ab) = (√a)(√b)

√180 = √(36 x 5) = (√36)(√5) = 6√5
√45 = √(9 x 5) = (√9)(√5) = 3√5
√135 = √(9 x 15) = (√9)(√15) = 3√15

So, \(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\) = (6√5 + 3√5)/(3√15)

= (9√5)/(3√15)
= 3/(√3)

Check the answer choices....not there!
We must rationalize the denominator.
Take 3/(√3) and multiply numerator and denominator by √3 to get: (3√3)/3, which simplifies to √3

Answer: A
General Discussion
avatar
Somnath09
avatar
Joined: 01 Apr 2017
Last visit: 07 Dec 2022
Posts: 2
Given Kudos: 288
Posts: 2
Kudos: 0
(180^(1/2) +45^(1/2))/135^(1/2) 25 Apr 2017, 06:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Why not B. 3/sqrt 3 is in B

Sent from my XT1068 using GMAT Club Forum mobile app
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 31 Oct 2025
Posts: 6,733
Own Kudos:
36,447
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,733
Kudos: 36,447
(180^(1/2) +45^(1/2))/135^(1/2) 25 Apr 2017, 06:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Somnath09
Why not B. 3/sqrt 3 is in B

Sent from my XT1068 using GMAT Club Forum mobile app
Show more

Here's another way to think of it.
We know that (sqrt 3)(sqrt 3) = 3, so let's replace the numerator, 3, with (sqrt 3)(sqrt 3)

We get: 3/sqrt 3 = (sqrt 3)(sqrt 3)/(sqrt 3) =sqrt 3

Cheers,
Brent
avatar
umadurga
avatar
Joined: 05 Nov 2016
Last visit: 02 Dec 2018
Posts: 60
Own Kudos:
45
Given Kudos: 18
Posts: 60
Kudos: 45
(180^(1/2) +45^(1/2))/135^(1/2) 25 Apr 2017, 19:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Taking \(\sqrt{45}\) common from numerator and denominator
\(\sqrt{45}\)(\(\sqrt{4}\)+1) / \(\sqrt{45}\)*(\(\sqrt{3}\))
(2+1)/\(\sqrt{3}\)
3/\(\sqrt{3}\)
\(\sqrt{3}\)
User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,974
Own Kudos:
8,710
 [4]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,974
Kudos: 8,710
 [4]
(180^(1/2) +45^(1/2))/135^(1/2) 28 Apr 2017, 15:15
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Bunuel
\(\frac{\sqrt{180}+\sqrt{45}}{\sqrt{135}}\)

A. \(\sqrt{3}\)

B. \(3\sqrt{3}\)

C. \(5\sqrt{3}\)

D. \(3\sqrt{5}\)

E. \(5\sqrt{5}\)
Show more

We can start by simplifying √180, √45, and √135:

√180 = √36 x √5 = 6√5

√45 = √9 x √5 = 3√5

Thus, 6√5 + 3√5 = 9√5.

√135 = √9 x √15 = 3√15

We now have:

(9√5)/(3√15) = 3/√3

Finally, we rationalize the denominator, getting:

(3/√3)(√3/√3) = 3√3/3 = √3

Answer: A
User avatar
BlueRocketAsh
User avatar
Joined: 11 Oct 2019
Last visit: 28 Aug 2020
Posts: 76
Own Kudos:
13
Given Kudos: 2
Posts: 76
Kudos: 13
(180^(1/2) +45^(1/2))/135^(1/2) 30 Jun 2020, 15:50
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(√180 - √45)/√135 = (6√5 - 3√5)/3√15
= 9√5 / 3√15
= 3 / √3
= √3
Answer A
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,962
Own Kudos:
1,117
Posts: 38,962
Kudos: 1,117
(180^(1/2) +45^(1/2))/135^(1/2) 04 Nov 2025, 17:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109763 posts
Krunaal
Tuck School Moderator
853 posts