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firas92
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![Which of the following values is greater than [m]\sqrt{2}[/](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "Which of the following values is greater than [m]\sqrt{2}[/"){kind=icon}
10 Jun 2021, 10:18
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
52% (01:49) correct
48%
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wrong
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Which of the following values is greater than \(\sqrt{2}\)?
i. \(\sqrt[3]{3}\)
ii. \(\sqrt[4]{4}\)
iii. \(\sqrt[5]{5}\)
A. i only
B. ii only
C. iii only
D. i and iii
E. i, ii and iii
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i. \(\sqrt[3]{3}\)
ii. \(\sqrt[4]{4}\)
iii. \(\sqrt[5]{5}\)
A. i only
B. ii only
C. iii only
D. i and iii
E. i, ii and iii
Posted from my mobile device
firas92
Current Student
Joined: 16 Jan 2019
Last visit: 02 Dec 2024
Posts: 617
Given Kudos: 142
Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
WE:Sales (Other)
Products:
12 Jun 2021, 11:04
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\(\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{3}{6}}=8^{\frac{1}{6}}\)
And, \(\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{2}{4}}=4^{\frac{1}{4}}\)
And, \(\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{5}{10}}=32^{\frac{1}{10}}\)
i. \(\sqrt[3]{3}=3^{\frac{1}{3}}=3^{\frac{2}{6}}=9^{\frac{1}{6}}\)
So i is greater than \(\sqrt{2}\)
ii. \(\sqrt[4]{4}=4^{\frac{1}{4}}\)
So ii is not greater than \(\sqrt{2}\)
iii. \(\sqrt[5]{5}=5^{\frac{1}{5}}=5^{\frac{2}{10}}=25^{\frac{1}{10}}\)
So iii is not greater than \(\sqrt{2}\)
Answer is (A)
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And, \(\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{2}{4}}=4^{\frac{1}{4}}\)
And, \(\sqrt{2}=2^{\frac{1}{2}}=2^{\frac{5}{10}}=32^{\frac{1}{10}}\)
i. \(\sqrt[3]{3}=3^{\frac{1}{3}}=3^{\frac{2}{6}}=9^{\frac{1}{6}}\)
So i is greater than \(\sqrt{2}\)
ii. \(\sqrt[4]{4}=4^{\frac{1}{4}}\)
So ii is not greater than \(\sqrt{2}\)
iii. \(\sqrt[5]{5}=5^{\frac{1}{5}}=5^{\frac{2}{10}}=25^{\frac{1}{10}}\)
So iii is not greater than \(\sqrt{2}\)
Answer is (A)
Posted from my mobile device
General Discussion
12 Jun 2021, 18:31
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Isn't \(\sqrt[3]{3}^{3}\) = 3?
By doing that, I got \(\sqrt[3]{5}\) as the only possible value greater than \(\sqrt{2}\)..
Any advice?
By doing that, I got \(\sqrt[3]{5}\) as the only possible value greater than \(\sqrt{2}\)..
Any advice?
