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If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the

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If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the [#permalink] New post 10 Oct 2005, 07:03
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A
B
C
D
E

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-root-4-cube-root-4-fourth-root-4-then-the-93340.html
[Reveal] Spoiler: OA
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 [#permalink] New post 10 Oct 2005, 07:39
Does this need some clarification? I do not understand the question. Should there be some sort of vaule in front of ^?
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 [#permalink] New post 10 Oct 2005, 07:43
I couldn't understand the question -

by ^3sqrt(4) - you mean cube root of 4?

Thanks.
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yes [#permalink] New post 10 Oct 2005, 08:07
I didn't know how to type it properly.

it's the cubed root of sqr rt of 4 and the 4th root of sqrt of 4

so it's square root of 4 plus the raised power 3 in front of the sq. rt of 4 plus the raised power 4 in front of the sq. rt of 4.

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 [#permalink] New post 10 Oct 2005, 08:22
E greater than 4...

2+1.41+~1=~4.4
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 [#permalink] New post 10 Oct 2005, 08:28
2 + sqrt(2) + cube root(2) = 2 + 1.41 + sqrt(1.41) = 2+1.41 + 1.xxx

so more than 4

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Re: if m = sqrt(4) + ^3sqrt(4) + ^4sqrt(4), then M is a. less [#permalink] New post 24 Jul 2013, 02:31
Answer should be E as ^3sqrt(4) + ^4sqrt(4) are both greater than 1
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the [#permalink] New post 24 Jul 2013, 02:43
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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

Here is a little trick: any positive integer root from a number more than 1 will be more than 1.

For instance: \sqrt[1000]{2}>1.

Hence \sqrt[3]{4}>1 and \sqrt[4]{4}>1 --> M=\sqrt{4}+\sqrt[3]{4}+\sqrt[4]{4}=2+(number \ more \ then \ 1)+(number \ more \ then \ 1)>4

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-root-4-cube-root-4-fourth-root-4-then-the-93340.html
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Re: If M=(root)(4)+(cube root)(4)+(fourth root)(4), then the   [#permalink] 24 Jul 2013, 02:43
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