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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
24^(1/2) - 16^(1/2) - 6^(1/2) =
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20 Mar 2020, 23:11
20 Mar 2020, 23:11
Expert Reply
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Question Stats:
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\(\sqrt{24} - \sqrt{16} - \sqrt{6} =\)
(A) \(\sqrt{6} - 4\)
(B) \(4 - 2 \sqrt{2}\)
(C) \(2\)
(D) \(\sqrt{6}\)
(E) \(2\sqrt{2}\)
(A) \(\sqrt{6} - 4\)
(B) \(4 - 2 \sqrt{2}\)
(C) \(2\)
(D) \(\sqrt{6}\)
(E) \(2\sqrt{2}\)
Re: 24^(1/2) - 16^(1/2) - 6^(1/2) =
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20 Apr 2020, 03:54
20 Apr 2020, 03:54
1
sqrt(24) = 2sqrt(6)
sqrt(16) = 4
sqrt(24) - sqrt(16) - sqrt(6)
2sqrt(6) -4 - sqrt(6)
sqrt(6) - 4
Hence, A is the Answer.
sqrt(16) = 4
sqrt(24) - sqrt(16) - sqrt(6)
2sqrt(6) -4 - sqrt(6)
sqrt(6) - 4
Hence, A is the Answer.
MyGuru Representative
Joined: 09 Apr 2020
Posts: 35
Given Kudos: 0
Re: 24^(1/2) - 16^(1/2) - 6^(1/2) =
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21 Apr 2020, 18:55
21 Apr 2020, 18:55
2
Expert Reply
GeminiHeat wrote:
\(\sqrt{24} - \sqrt{16} - \sqrt{6} =\)
(A) \(\sqrt{6} - 4\)
(B) \(4 - 2 \sqrt{2}\)
(C) \(2\)
(D) \(\sqrt{6}\)
(E) \(2\sqrt{2}\)
(A) \(\sqrt{6} - 4\)
(B) \(4 - 2 \sqrt{2}\)
(C) \(2\)
(D) \(\sqrt{6}\)
(E) \(2\sqrt{2}\)
If you're not comfortable working with roots, estimation works well in this problem.
\(\sqrt{24}\) is a little less than 5
\(\sqrt{16}\) is 4
\(\sqrt{6}\) is between 2 and 3. Let's say it's around 2.5
So, estimating, we have approximately 5 -4 - 2.5
The answer has to be negative, which immediately rules out C, D, and E.
B can be ruled out too, since \(2 \sqrt{2}\) has to be less than 4, so B is positive as well.
For choice A, 2.5 - 4 is clearly negative, so it fits.
Answer: A
