Square Root Properties

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daflower: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Sun Jul 18, 2010 11:45 am

Square Root Properties

by daflower » Sun Jul 18, 2010 11:51 am

Really stumped on solving this one - came across it in a practice test.

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?

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Source: Beat The GMAT — Problem Solving | Sun Jul 18, 2010 11:51 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pm; Thanked: 215 times; Followed by:7 members

by kvcpk » Sun Jul 18, 2010 11:57 am

daflower wrote:Really stumped on solving this one - came across it in a practice test.

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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kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 am; Location: London; Thanked: 70 times; Followed by:3 members

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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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

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.

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).