MGMAT CAT - Root of a Square

[cuty]

If,LHS whole term in square root((x+4)^2)= 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5

hey guys i knw how to solve it like taking square of both sides so we can easily find out the value of but i want to knw why dont i solve it the following way
* IF we cancel out root wid power then we left wid x+4=3, x=-1.....why don"t we do dis way
I mean if we take square root of 4 , simply our ans is 2 So why we partial wid dat one ??

[HSPA]

How to solve this..Kindly explain
I got two values for X i.e. x= -1 and x= -7
sqrt(x^2) = |x| = +x / -x

[cuty]

hey HSPA, can we do like this..sqrt(x+4)(x+4) then take out (x+4)=3

[Stuart@KaplanGMAT]

If,LHS whole term in square root((x+4)^2)= 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5

hey guys i knw how to solve it like taking square of both sides so we can easily find out the value of but i want to knw why dont i solve it the following way
* IF we cancel out root wid power then we left wid x+4=3, x=-1.....why don"t we do dis way
I mean if we take square root of 4 , simply our ans is 2 So why we partial wid dat one ??

Based on the question, we know there are at least two values for x.

...which of the following could be the value of x - 4?

If there were only 1 possible value, the GMAT wouldn't use the word "could".

We also see squares and roots, alerting us to a positive and negative solution.

Now, let's put on our GMAT question writer hats for a moment: if we have an equation with 2 possible solutions, and only one is going to appear in the choices, should the right answer be the obvious solution or the subtle one? Why, the subtle one, of course, since we want to reward test takers who see every solution to a problem, not just the obvious one!

So, to save ourselves time on test day, we shouldn't even bother solving the "obvious" side - we should focus on, to paraphrase Robert Frost, the solution less travelled.

sqrt((x+4)^2)= 3
(x+4)^2 = 9
(x+4) = +/- 3
(x+4) = -3 (the less obvious solution)
x = -7

Now, here's where the unwary test taker makes another mistake - choosing the right answer to the wrong question, one of the most common GMAT traps. Step 4 of the Kaplan Method for Problem Solving is "double check the question" - we now realize that the question is "what's a possible value of (x-4)", so one final step:

x = -7
x - 4 = -7 - 4 = -11

choose A!

[HSPA]

hey HSPA, can we do like this..sqrt(x+4)(x+4) then take out (x+4)=3

Easy way: square on both sides

(x+4)^2 = 3^2
We know a^2 - b^2 = a+b * a-b
(x+4)^2 - 3^2 = 0 => (x+4-3)(x+4+3) = 0 => x = -1 or x = -7

since square of a positve and negitive integer is always +ve ... square for both (-7+4) and (-1+4) will be same...

Considering only one side (x+4) = 3 you took -1+4 = 3 but 'magnitude' of -7+4 is also 3

[GMATGuruNY]

)=

If,LHS whole term in square root((x+4)^2)= 3, which of the following could be the value of x - 4?

-11
-7
-4
-3
5

hey guys i knw how to solve it like taking square of both sides so we can easily find out the value of but i want to knw why dont i solve it the following way
* IF we cancel out root wid power then we left wid x+4=3, x=-1.....why don"t we do dis way
I mean if we take square root of 4 , simply our ans is 2 So why we partial wid dat one ??

We can plug in the answer choices, which represent the value of x-4.
One of the values of x must be 4 more than the correct answer choice.
Adding 4 to each answer choice, we get the following possible values for x:

A) -11+4 = -7
B) -7 + 4 = -3
C) -4 + 4 = 0
D) -3 + 4 = 1
E) 5+4 = 9

Scanning the results above, we can see that only x = -7 works:
√((x+4)² = √((-7+4)² = √(-3)² = √9 = 3.

The correct answer is A.