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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
If M = 4^(1/2) + 4^(1/3) + 4^(1/4), then the value of M is:
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29 Nov 2022, 08:46
29 Nov 2022, 08:46
Expert Reply
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Question Stats:
63% (02:11) correct
36% (01:55) wrong based on 11 sessions
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If \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\), then the value of M is:
A. Less than 3
B. Equal to 3
C. Between 3 and 4
D. Equal to 4
E. Greater than 4
A. Less than 3
B. Equal to 3
C. Between 3 and 4
D. Equal to 4
E. Greater than 4
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: If M = 4^(1/2) + 4^(1/3) + 4^(1/4), then the value of M is:
[#permalink]
30 Nov 2022, 23:08
30 Nov 2022, 23:08
Expert Reply
\(M=4^{1/2} + 4^{1/3} + 4^{1/4}\)
Now we know that \(4^{1/2} = 2\)
We also know that \(4^{1/4} = \sqrt{2} \approx 1.414 > 1\)
And finally \(4^{1/3} > 4^{1/4} \Rightarrow 4^{1/3}>1\)
So combining all three together \(M > 2+1+1 \Rightarrow M > 4\)
Answer: E
Now we know that \(4^{1/2} = 2\)
We also know that \(4^{1/4} = \sqrt{2} \approx 1.414 > 1\)
And finally \(4^{1/3} > 4^{1/4} \Rightarrow 4^{1/3}>1\)
So combining all three together \(M > 2+1+1 \Rightarrow M > 4\)
Answer: E
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Re: If M = 4^(1/2) + 4^(1/3) + 4^(1/4), then the value of M is:
[#permalink]
14 Jan 2023, 23:03
14 Jan 2023, 23:03
Given that \(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\) and we need to find the value of M
\(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\)
=> M = 2 + \(\sqrt[3]{4} + 2^(2/4)\) = 2 + \(\sqrt[3]{4} + \sqrt[2]{2}\)
Now, \(\sqrt[3]{4}\) will be between 1 and 2 as \(1^3\) = 1 and \(2^3\) = 8
\(\sqrt[2]{2}\) = 1.414
=> M = 2 + 1.414 + number between 1 and 2
=> M > 2 + 1.414 + 1
=> M > 4.414
So, Answer will be E
Hope it helps!
\(M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}\)
=> M = 2 + \(\sqrt[3]{4} + 2^(2/4)\) = 2 + \(\sqrt[3]{4} + \sqrt[2]{2}\)
Now, \(\sqrt[3]{4}\) will be between 1 and 2 as \(1^3\) = 1 and \(2^3\) = 8
\(\sqrt[2]{2}\) = 1.414
=> M = 2 + 1.414 + number between 1 and 2
=> M > 2 + 1.414 + 1
=> M > 4.414
So, Answer will be E
Hope it helps!
