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If X = SqrRoot(4) + CubeRoot(4) + FourthRoot(4), then the

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Director
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If X = SqrRoot(4) + CubeRoot(4) + FourthRoot(4), then the [#permalink] New post 09 Sep 2007, 15:01
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A
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C
D
E

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If X = SqrRoot(4) + CubeRoot(4) + FourthRoot(4), then the value of X is

a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4

- Brajesh
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 [#permalink] New post 09 Sep 2007, 15:44
I would say greater than 4..

sqrt(4)=2

cubert(4)=sqrt(2)=1.41

forthrt(4)=sqrt(1.41) approx=1

2+1.41+1=4.41
Director
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Re: PS - Value of X [#permalink] New post 09 Sep 2007, 16:36
b14kumar wrote:
If X = SqrRoot(4) + CubeRoot(4) + FourthRoot(4), then the value of X is

a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4

- Brajesh


X = SqrRoot(4) + CubeRoot(4) + FourthRoot(4)
X = 2 + 1.xxxxx + 1.xxxxxxxxxxx
X = 4.xxxxxxxxxx

so E. grater than 4.
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 [#permalink] New post 09 Sep 2007, 22:26
4^1/2 = 2
4^1/3 = between 1 and 2 since cuberoot(8) = 2
4^1/4 = 2^1/2 = 1.4


4^1/2 + 4^1/4 = ~3.3. So we can rule out A,B,C and D since 4^1/4 != 1. So E must be it.
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Re: PS - Value of X [#permalink] New post 09 Sep 2007, 22:36
[quote="b14kumar"]If X = SqrRoot(4) + CubeRoot(4) + FourthRoot(4), then the value of X is

a) less than 3
b) equal to 3
c) between 3 and 4
d) equal to 4
e) greater than 4

- Brajesh[/quote]

SqrRoot(4)=2
CubeRoot(1)=1<CubeRoot(4)<CubeRoot(8)=2
FouthRoot(1)=1<FouthRoot(4)<FouthRoot(16)=2
If we take minimum, we have 2+(1,..)+(1,..)=(4,..) => So greater than 4 (E)
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 [#permalink] New post 10 Sep 2007, 06:35
The equation can be simplified as

Sqrt(4) + Cube root ( 4) + 4th root ( 4)

2 + <2 + Sqrt(2)

3.4 + <2

So greater than 4
  [#permalink] 10 Sep 2007, 06:35
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