Square Root Properties

Expert replies

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

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?

Like this post

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 pmFollowed by: 7 members; Thanked: 215 times

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.

Like this post

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

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

Like this post

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; 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).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review