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confusion in solving this gmat prob

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by quantskillsgmat » Mon Jan 09, 2012 10:47 pm
can anyone explain me why square root of x is always taken as positive in GMAT
eg
Q SQUARE ROOT OF 4+CUBE ROOT OF 4+FORUTH ROOT OF 4 is
a)between 1 and 2
b)between 2 and 3
c)between 3 and 4
d)more than 4
here if i take positive roots then ans is more than 4 but if i consider both positive and negative various ans are possible.
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by neelgandham » Mon Jan 09, 2012 11:01 pm
As far as I know

The term 'Square root' in GMAT is used to refer to the principal square root(The positive square root). Check the properties section here -> https://en.wikipedia.org/wiki/Square_root for more information regarding principal square root.

Why is it referred to the principal square root ? I really don't know. We shall wait for the experts to answer.
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by Anurag@Gurome » Mon Jan 09, 2012 11:09 pm
quantskillsgmat wrote:can anyone explain me why square root of x is always taken as positive in GMAT...
There is a difference between square root of x and √x. Any number x have two square roots, a negative one and a positive one, i.e. √x and -√x. But √x always represents only the positive root.

For example, 4 have two square roots 2 and - 2. But √4 = 2 not -2.

If the question says square root of 4, then your logic is correct. But I believe the question says √4. Hence, only the positive root has to be considered.

Similarly, any number x has four fourth roots, one positive, one negative, and two imaginary roots. But if the symbol of fourth root is used, then we have to take the positive roots only.
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by archit.job » Sat Jan 14, 2012 1:28 am
Dear Anurag Sir,

I would like to confirm one thing..that if √4 = +2 & squareroot 4 =±2 agreed,

but we cannot say that √-4 =-2 it has to be a complex output.
So how can √4 be = only +4
Kindly explain.
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