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If M = \sqrt4 + \sqrt 4 + \sqrt 4 then M is A) less than 3

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If M = \sqrt4 + \sqrt 4 + \sqrt 4 then M is A) less than 3 [#permalink]

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New post 18 Aug 2008, 14:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4
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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 14:13
brokerbevo wrote:
If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4


E.

This is going to be \(2 + \sqrt[3]4 + \sqrt{2}\)

We know that \(\sqrt{2}\) is approx 1.4, so 2 + 1.4 = 3.4 and the cube root of 4 should be between the two other values, so we have 2 + 1.4 + [some value between 2 and 1.4] therefore, it must be greater than 4.
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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 14:14
brokerbevo wrote:
If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4


sqrt(2)~1.41
2 + 2* sqrt(2) + sqrt(2) --> 2+ 2*1.4 +1.4 > 4

E.
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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 14:16
\(\sqrt[3]4\)≠\(2\sqrt{2}\)

The cube root cannot be greater than the square root.

x2suresh wrote:
brokerbevo wrote:
If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4


sqrt(2)~1.41
2 + 2* sqrt(2) + sqrt(2) --> 2+ 2*1.4 +1.4 > 4

E.

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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 14:19
jallenmorris wrote:
\(\sqrt[3]4\)≠\(2\sqrt{2}\)
x2suresh wrote:
brokerbevo wrote:
If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4


sqrt(2)~1.41
2 + 2* sqrt(2) + sqrt(2) --> 2+ 2*1.4 +1.4 > 4

E.


you are right.. thanks for pointing out.

it should be Power 2/3 I took it as power 3/2
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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 14:20
It's a small point in this question. Just hope it helps you in the future for another question. You still had the right answer!
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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 15:02
brokerbevo wrote:
If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4


the nth root of any number greater than 1 is always greater than 1.

Therefore, E

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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 15:04
That rule eliminates A & B, but doesn't really help you decide between C, D, and E.

zoinnk wrote:
brokerbevo wrote:
If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4


the nth root of any number greater than 1 is always greater than 1.

Therefore, E

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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 15:16
The numbers can be simplified to 2 + sqrt(2) + (2^2/3); I went the long way...sqrt(2) ~ 1.414; (2^2/3) ~ 1.6; Sum of all these terms is > 4; So, E.

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Re: roots of 4 [#permalink]

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New post 18 Aug 2008, 20:39
jallenmorris wrote:
That rule eliminates A & B, but doesn't really help you decide between C, D, and E.

zoinnk wrote:
brokerbevo wrote:
If M = \(\sqrt4 + \sqrt[3]4 + \sqrt[4]4\) then M is

A) less than 3
B) equal to 3
C) between 3 and 4
D) equal to 4
E) greater than 4


the nth root of any number greater than 1 is always greater than 1.

Therefore, E


I assumed that anyone would realize sqrt(4) is 2...

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Re: roots of 4 [#permalink]

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New post 19 Aug 2008, 04:49
Sometimes people that read it might not see exactly what you're saying, and for the sake of learning, it's often best to just spell it out even when it appears obvious. For those people who do not see it as obvious aren't likely to speak out and say they don't understand. By stating what might appear to be obvious on how the rule brings us to the answer step-by-step, it helps people learn. Some users don't care to hit a 750+ GMAT score. They just want to go from a 550 to a 620 maybe and they'll be happy. We want to help those individuals as well.
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Re: roots of 4   [#permalink] 19 Aug 2008, 04:49
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If M = \sqrt4 + \sqrt 4 + \sqrt 4 then M is A) less than 3

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