What is the value of \(\frac{2}{2-\sqrt{2}}? \)
(A) 1
(B) 2
(C) 1 + \(\sqrt{2}\)
(D) 2 + \(\sqrt{2}\)
(E) 4
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
What is the value of 2/(2−√2)?
This topic has expert replies
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
We have \(\frac{2}{2-\sqrt{2}}\)M7MBA wrote:What is the value of \(\frac{2}{2-\sqrt{2}}? \)
(A) 1
(B) 2
(C) 1 + \(\sqrt{2}\)
(D) 2 + \(\sqrt{2}\)
(E) 4
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
Let's rationalize the denominator
Multiplying \(\frac{2}{2-\sqrt{2}}\) by \(\frac{2+\sqrt{2}}{2+\sqrt{2}}\); this will not chnage the value of the fraction.
\(\frac{2}{2-\sqrt{2}}\) * \(\frac{2+\sqrt{2}}{2+\sqrt{2}}\)
\(\frac{4+2\sqrt{2}}{2^2-\sqrt{2^2}}\)
\(\frac{4+2\sqrt{2}}{4-2}\)
\(\frac{4+2\sqrt{2}}{2}\)
\(2+\sqrt{2}\)
The correct answer: D
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: GRE Manhattan | ACT Tutoring San Francisco | IELTS Prep Courses Austin | Seattle IELTS Tutoring | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7245
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
M7MBA wrote:What is the value of \(\frac{2}{2-\sqrt{2}}? \)
(A) 1
(B) 2
(C) 1 + \(\sqrt{2}\)
(D) 2 + \(\sqrt{2}\)
(E) 4
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
We can simplify the expression by multiplying by (2 + √2)/(2 + √2), and we have:
(4 + 2√2)/(2^2 - (√2)^2)
(4 + 2√2)/(4 - 2)
(4 + 2√2)/2
2 + √2
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7245
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
M7MBA wrote:What is the value of \(\frac{2}{2-\sqrt{2}}? \)
(A) 1
(B) 2
(C) 1 + \(\sqrt{2}\)
(D) 2 + \(\sqrt{2}\)
(E) 4
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
We can simplify the expression by multiplying by (2 + √2)/(2 + √2), and we have:
(4 + 2√2)/(2^2 - (√2)^2)
(4 + 2√2)/(4 - 2)
(4 + 2√2)/2
2 + √2
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews