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Square Root Properties

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by kvcpk » Sun Jul 18, 2010 11:57 am
daflower wrote:Really stumped on solving this one - came across it in a practice test.

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I wasted a lot of time using trial & error to determine the cube root of 4 and the quad (?) root of 4.
Anyone have a shortcut?
m=2+3rdroot(4)+4throot(4)
m=2+3rdroot(4)+squareroot(2)
m=2+3rdroot(4)+1.414
m=3.414+3rdroot(4)
square root of 4 is 2 and 4th root of 4 is 1.41. So 3rd wot of 4 will be in between these two.
So m should be greater than 4.

pick E.
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by kmittal82 » Sun Jul 18, 2010 12:01 pm
Might not the best way, but here's a shot

(4)^1/2 + (4)^1/3 + (4)^1/4

= 2 + (4^1/2)^1/2 + (2^2)^1/3

= 2 + 2^1/2 + (2)^2/3

Now, 2^1/2 = 1.414, and 2^2/3 is some quantity greater than 1.414 (since 2/3 is greater than 1/2)

Now, we know that the expression is 3.414 + some quantity greater than 1.414 and less than 2

So, the value is atleast 4.8, plus another small number.

Hence, only (E) remains
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by Stuart@KaplanGMAT » Sun Jul 18, 2010 1:24 pm
daflower wrote:Really stumped on solving this one - came across it in a practice test.

Image


I wasted a lot of time using trial & error to determine the cube root of 4 and the quad (?) root of 4.
Anyone have a shortcut?
Keeping an eye on the answer choices makes this a very fast question.

The (any root greater than 1) of (any number greater than 1) is going to be greater than 1. (Say that 10 times fast!)

So:

sqrt4 = 2
cuberoot4 > 1
quardicroot4 > 1

sum > 2 + 1 + 1

sum > 4... choose (E).
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