If, sq root (x+4)^2 = 3 the what is x-4
a. -11
b. -7
c. -4
d. -3
e. 5

May be, I am right.
Ignore...

What is confusing to you? You'll get more out of the forums if you actually explain what your thinking is and where you got lost, or which part of the explanation doesn't make sense to you.

So we've got a complicated expression on the left-side of that eqn:

SQRT[(x+4)^2]

You may want to write that out on a piece of paper, as it looks annoying on screen.

When you take the square root of a squared expression, there are two possibilities: what's inside the parentheses may be positive, and what's inside the parentheses may be negative. For example:

SQRT[3^2] = SQRT 9 = 3
SQRT[(-3)^2)] = SQRT 9 = 3

So I have to take both possibilities into account when simplifying. If I replace 3 with x in the above, I get:
SQRT[x^2]
I don't know whether x is positive or negative, but both options can lead to the same outcome (just like 3 and -3 will give me the same answer in my numerical example above).

So when I rewrite SQRT[x^2], I always take into account two possibilities:
x
and
-x

Similarly, on this problem, we have the expression x+4. That entire expression could be positive or negative, so I could have:
x+4 = 3
or
-(x+4) = 3

I glance at the answers and see 4 negative numbers. Also, I know that if someone makes a mistake in the above step, they're going to forget the negative option, not the positive one. Both of those reasons mean that I'd rather try the negative option first - because it's easy to forget or overlook that, so that's how people will get this one wrong.

-(x+4) = 3
divide both sides by -1
x+4 = -3
x = -7

NOT answer B! They didn't ask for x. They asked for x-4.
-7-4 = -11
Answer A.

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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT