GRE Prep 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.
Which of the following equals
[#permalink]
09 Aug 2017, 15:23
09 Aug 2017, 15:23
Expert Reply
2
Bookmarks
00:00
Question Stats:
88% (01:10) correct
11% (02:04) wrong based on 195 sessions
Hide Show timer Statistics
Which of the following equals \(- ( \sqrt{2} - \sqrt{8} ) ( 2 \sqrt{2} + \sqrt{8} )\) ?
A. \(-8 \sqrt{2}\)
B. -4
C. 4
D. \(4 \sqrt{2}\)
E. 8
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following equals
[#permalink]
12 Aug 2017, 06:03
12 Aug 2017, 06:03
2
2
Bookmarks
Carcass wrote:
Which of the following equals \(- ( \sqrt{2} - \sqrt{8} ) ( 2 \sqrt{2} + \sqrt{8} )\) ?
A. \(-8 \sqrt{2}\)
B. -4
C. 4
D. \(4 \sqrt{2}\)
E. 8
A. \(-8 \sqrt{2}\)
B. -4
C. 4
D. \(4 \sqrt{2}\)
E. 8
Let's apply the FOIL method.
We'll also use the fact that (√a)(√b) = √(ab)
So, -(√2 - √8)(2√2 + √8) = -(2√4 + √16 - 2√16 - √64)
= -(4 + 4 - 8 - 8)
= -(-8)
= 8
Answer: E
Re: Which of the following equals
[#permalink]
04 May 2020, 03:15
04 May 2020, 03:15
1
A shortcut to this is to consider root(2) instead of 2root(2) in the second bracket. Using a^2 - b^2 = (a+b)(a-b) formula, we get -[2-8] = -(-6) = 6
Now when we multiply 2 numbers, A * B, if B increases, then the total product increases too.
The initial product value is 6, but we add one more root(2) to B, so the total product value should be more than 6. The minus sign outside the product in the question makes it invariably positive.
The only option greater than 6 is 8. (E)
Now when we multiply 2 numbers, A * B, if B increases, then the total product increases too.
The initial product value is 6, but we add one more root(2) to B, so the total product value should be more than 6. The minus sign outside the product in the question makes it invariably positive.
The only option greater than 6 is 8. (E)
