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## Need expert help

tagged by: Brent@GMATPrepNow

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voodoo_child GMAT Destroyer!
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Need expert help Mon Apr 30, 2012 7:40 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
Find the solution of Sqrt(2+sqrt(2+sqrt(2+sqrt(.........

Here's what I did:

sqrt(2+x)=x
Therefore, 2+x=x^2
Therefore, x^2 - x - 2 => (x-2) (x+1)=0
X = 2 or -1.

Correct answer is 2; I am not able to rule out (-1). Any help? Thanks

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aneesh.kg GMAT Destroyer!
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Mon Apr 30, 2012 7:43 am
Square root of any quantity is always positive.
Since x is square root of a quantity here, the negative value (-1) is ruled out.

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Aneesh Bangia
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aneesh.bangia@gmail.com

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Brent@GMATPrepNow GMAT Instructor
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Mon Apr 30, 2012 9:00 am
voodoo_child wrote:
Find the solution of Sqrt(2+sqrt(2+sqrt(2+sqrt(.........

Here's what I did:

sqrt(2+x)=x
Therefore, 2+x=x^2
Therefore, x^2 - x - 2 => (x-2) (x+1)=0
X = 2 or -1.
Correct answer is 2; I am not able to rule out (-1). Any help? Thanks
When you solve a question involving square roots, you should plug in the answers to check for extraneous roots (aka, solutions that don't work).

x=2: sqrt(2+2)=2 (WORKS)
x=-1: sqrt(2+(-1))=-1 (DOESN'T WORK)

Cheers,
Brent

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voodoo_child GMAT Destroyer!
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Mon Apr 30, 2012 12:06 pm
Brent@GMATPrepNow wrote:
x=2: sqrt(2+2)=2 (WORKS)
x=-1: sqrt(2+(-1))=-1 (DOESN'T WORK)

Cheers,
Brent
Brent and Aneesh - question - Sqrt (1) is not equal to -1? Why? (-1)^2 =1. Therefore, Sqrt(1) = 1 or -1. Correct?

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Mon Apr 30, 2012 12:13 pm
voodoo_child wrote:
Brent@GMATPrepNow wrote:
x=2: sqrt(2+2)=2 (WORKS)
x=-1: sqrt(2+(-1))=-1 (DOESN'T WORK)

Cheers,
Brent
Brent and Aneesh - question - Sqrt (1) is not equal to -1? Why? (-1)^2 =1. Therefore, Sqrt(1) = 1 or -1. Correct?
By definition, sqrt(n) denotes the positive number whose square is n.
Similarly, -sqrt(n) denotes the negative number whose square is n.

So, the takeaway here is that the equation x^2 = 9 has 2 solutions (x = 3, -3), while the equation sqrt(9)= x has only 1 solution (x = 3)

Cheers,
Brent

_________________
Brent Hanneson - GMAT Prep Now instructor
- Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
- Use our video course in conjunction with
- Watch hours of free videos on DS, RC and AWA
- Our top 3 free videos:
1) The Double Matrix method
3) Managing your time on the GMAT

Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
aneesh.kg GMAT Destroyer!
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Mon Apr 30, 2012 12:44 pm
By definition, when the symbol of 'square root' is placed over a quantity, the output must be positive. Notice that you don't get two values when you take the square root of a number on your calculator.

To clear your confusion, let's take this example:

say x^2 = 9
Step1: x = +/- sqrt(9)
Step2: Since sqrt(9) = 3,
Step3: x = +/- 3

So,
(i) if x^2 = any number, we get two values - one positive and one negative - of x
(ii) if x = sqrt(number), we get just one positive value of x

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Aneesh Bangia
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aneesh.bangia@gmail.com

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