General question about roots (Number properties)

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metalhead: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Sun Dec 27, 2009 12:11 pm; Thanked: 1 times

by metalhead » Thu Mar 18, 2010 3:38 pm

In the Manhattan GMAT 'Number Poperties' guide, in Chapter 6, it says that a square root has only one value (as far as GMAT is concerned). To quote from the book -

" If root_of(4) = x, what is x?
In the example, x=2, since (2)(2)= 4. While it is true that (-2)(-2)=4, the GMAT follows the standard convention that when we are taking an even root (a square root, a 4th root, a 6th root, etc), a radical (root) sign denotes only the non-negative root of an integer. Thus 2 is the only solution to x. -2 is NOT a solution."

How accurate is this statement that we only need to consider the positive root in this scenario on the actual exam?

Appreciate your help!

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Source: Beat The GMAT — Problem Solving | Thu Mar 18, 2010 3:38 pm

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Thu Mar 18, 2010 10:26 pm

i follow only one rule i.e if its a square or square root of a number then we have to take +ve value
and if its for a variable then bth are true

so v4=x---->x=2(becoz 4 is a number)
and x^2=4--->x=-/+ 2(bcoz x is a variable)

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Shawshank: Master | Next Rank: 500 Posts; Posts: 305; Joined: Mon Jul 27, 2009 5:38 am; Thanked: 10 times

by Shawshank » Thu Mar 18, 2010 10:47 pm

thephoenix wrote:i follow only one rule i.e if its a square or square root of a number then we have to take +ve value
and if its for a variable then bth are true

so v4=x---->x=2(becoz 4 is a number)
and x^2=4--->x=-/+ 2(bcoz x is a variable)

I have never heard of this rule.. so just confirming..

You mean IF x = sqrroot(4) ... then x = 2
IF x^2 = 4..............then x = -/+ 2

Is this what your trying to say..

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Shawshank Redemtion -- Hope is still alive ...

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Mar 19, 2010 12:58 am

Shawshank wrote:
thephoenix wrote:i follow only one rule i.e if its a square or square root of a number then we have to take +ve value
and if its for a variable then bth are true

so v4=x---->x=2(becoz 4 is a number)
and x^2=4--->x=-/+ 2(bcoz x is a variable)
I have never heard of this rule.. so just confirming..

You mean IF x = sqrroot(4) ... then x = 2
IF x^2 = 4..............then x = -/+ 2

Is this what your trying to say..

If a number x > 0, then on GMAT, âˆšx > 0 and -âˆšx < 0. This is taken so as to shut doors to any ambiguity.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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