Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 2807:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 28, 2026 - Oct. 16, 2027, 7:00pm-10:00pm EST
Sep 2911:00 AM EDT
-01:00 PM EDT
" Description: Top scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thur Sept. 29, 2026 - Dec. 3, 2026, 11:00am-1:00pm EST
Oct 0107:00 AM BST
-08:00 AM GMT
Welcome to the GMAT Club's Free Interview Prep Event for Top MBA Programs! Buy tickets - Virtual series that’s all set to equip you to -excel in your MBA interviews.
Oct 0301:00 PM EDT
-04:00 PM EDT
Top scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Saturdays Oct. 3, 2026 - Dec. 26, 2026, 1:00pm-4:00pm EST
22 Feb 2025, 01:02
Kudos
Bookmarks
x: 6
y: -3
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
56% (02:32) correct
44%
(02:35)
wrong
based on 363
sessions
History
Date
Time
Result
Not Attempted Yet
The number \(\sqrt{63-36√3}\) can be written in the form of x+y√3 for some integers x and y. Choose the values of x and y in the table which are consistent with the given information
| x | y | |
| -6 | ||
| -3 | ||
| 0 | ||
| 2 | ||
| 3 | ||
| 6 |
ShowHide Answer
Official Answer
x: 6
y: -3
23 Feb 2025, 10:39
Kudos
Bookmarks
Let's simplify \(\sqrt{63-36√3}\) to get to the form x+y√3
= \(\sqrt{9(7-4√3)}\)
= \(3\sqrt{(3+4-4√3)}\)
= \(3\sqrt{(2-√3)^2}\)
= \(3(2-√3)\) (Given 2>√3 and square root gives a positive number, so 2-√3>0)
= \(6-3√3\)
x = 6, y = -3
= \(\sqrt{9(7-4√3)}\)
= \(3\sqrt{(3+4-4√3)}\)
= \(3\sqrt{(2-√3)^2}\)
= \(3(2-√3)\) (Given 2>√3 and square root gives a positive number, so 2-√3>0)
= \(6-3√3\)
x = 6, y = -3
GMATinsight
Given that \(\sqrt{63-36√3}\) = x+y√3 .
Square both sides -> \(\sqrt{63-36√3}^2 = (x+y√3)^2 \)
=> 63-36√3 = \( x^2 + 3y^2 + 2√3xy \)
=> \( x^2 + 3y^2 = 63 \) and 2√3xy= -36√3
=> xy = -18 (possible options for x and y are 9,-2, ; 6,-3 ; 18,-1)
Please note that x needs to be positive and greater than y for the term x+y√3 to be positive. This term can't be negative since it is the square root of 63-36√3.
The only values that satisfy both equations xy = -18 and \( x^2 + 3y^2 = 63 \) are x = 6 and y = -3.
Hope this helps!
Square both sides -> \(\sqrt{63-36√3}^2 = (x+y√3)^2 \)
=> 63-36√3 = \( x^2 + 3y^2 + 2√3xy \)
=> \( x^2 + 3y^2 = 63 \) and 2√3xy= -36√3
=> xy = -18 (possible options for x and y are 9,-2, ; 6,-3 ; 18,-1)
Please note that x needs to be positive and greater than y for the term x+y√3 to be positive. This term can't be negative since it is the square root of 63-36√3.
The only values that satisfy both equations xy = -18 and \( x^2 + 3y^2 = 63 \) are x = 6 and y = -3.
Hope this helps!
