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Roots

by Buix0065 » Sat Jul 16, 2011 8:44 am
I am having a hard time with some baseline roots concepts.

In the below problem: if sq.root(x+4)^2 = 3 which could be a value of x - 4?
-11
-7
-4
-3
5



My inclination is to cancel the square root and the ^2 to get x + 4 = 3.

In the case of x = 1

sq.root(1+4)^2 = (1+4)

What is the difference that, in solving this problem gets me to square both sides:

(x+4)^2 = 9

I realize this is a pretty basic thing, so any insights to help re-set my frame of reference would be helpful!

OA[/spoiler]A
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by GMATGuruNY » Sat Jul 16, 2011 10:36 am
Buix0065 wrote:I am having a hard time with some baseline roots concepts.

In the below problem: if sq.root(x+4)^2 = 3 which could be a value of x - 4?
-11
-7
-4
-3
5

OA[/spoiler]A
We can plug in the answers, which represent the value of x-4.

Answer choice A: x-4 = -11.
Thus, x = -7.
Plugging x = -7 into the equation √(x+4)^2 = 3, we get:
√(-7+4)^2 = 3
√(-3)^2 = 3
√9 = 3
3 = 3. Success!

The correct answer is A.
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by beatthegmat.garry » Sat Jul 16, 2011 11:40 am
I completely understand your situation and recommend you to no fall in this pit. We have a tendency of taking a square root right ways on both side but remember a square root of a square results in one absolute value and 2 directions (sign).

Thus sq.root((x+4)^2) = 3 is always equal to +/- 3.

i.e. x+4=3 or x+4=-3
i.e. x=-1 or x=-7

hence (x-4)=-5 or (x-4)=-11 ...... (adding -4 on both sides of previous step)


We dont see -5 as the option and hence the only choice we have is -11.

I dont think GMAT will ever have 2 choices that possibly can be the answers.

Hope this helps and you never forget this property :)
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