If x does not equal 0, then square root of x^2/x =

[mukund.jagadish]

Source: GMAT Prep Test 1

If x does not equal 0, then square root of x^2/x =

a. -1
b. 0
c. 1
d. x
e. |x|/x

OA: E

Please advise, thanks.

[ryan.m.doyle]

Source: GMAT Prep Test 1

If x does not equal 0, then square root of x^2/x =

a. -1
b. 0
c. 1
d. x
e. |x|/x

OA: E

Please advise, thanks.

I saw this explanation on another board

Stuart Kovinsky -

The key to this question is recognizing that the sqrt symbol literally translates as "the positive square root of". So, if you saw a question that asks:

What's the sqrt(25), the answer would be ONLY +5.

Since we translate the notation in this manner, we know that, no matter the sign of x, sqrt(x^2) is always going to be positive. In other words, the numerator in the expression will be the absolute value of x.

So, we end up with:

|x|/x ... choose (5)

http://www.beatthegmat.com/if-x-0-then- ... 14328.html

[mschwrtz]

Just to clarify, the expression originally posted as "square root of x^2/x" should read "[square root of (x^2)]/x." If we read it as square root of [(x^2)/x], then none of the listed answers is correct. In fact, it would be even better to write, say, "[radical (x^2)]/x," to emphasize that the radical sign indicates the primary (positive) square root.

But--bottom line--Ryan and SK are correct: radical (x^2)=|x|.

[eduardo_holsch]

Hello, I think I understand the explanation, but I still have one question... and my thinking is as follows:

If we have (square root of x^2)/x, couldn't we square the whole fraction to get x^2/x^2... and this would equal 1 (regardless of the value of "x")?

Thanks in advance!

[RonPurewal]

Hello, I think I understand the explanation, but I still have one question... and my thinking is as follows:

If we have (square root of x^2)/x, couldn't we square the whole fraction to get x^2/x^2... and this would equal 1 (regardless of the value of "x")?

Thanks in advance!

you could, but that wouldn't tell you anything.
analogously, squaring -1/1 and squaring 1/1 will both give you 1/1, but that certainly doesn't mean that -1/1 and 1/1 are the same.

[mirzank]

Source: GMAT Prep Test 1

If x does not equal 0, then square root of x^2/x =

a. -1
b. 0
c. 1
d. x
e. |x|/x

OA: E

Please advise, thanks.

I saw this explanation on another board

Stuart Kovinsky -

The key to this question is recognizing that the sqrt symbol literally translates as "the positive square root of". So, if you saw a question that asks:

What's the sqrt(25), the answer would be ONLY +5.

Since we translate the notation in this manner, we know that, no matter the sign of x, sqrt(x^2) is always going to be positive. In other words, the numerator in the expression will be the absolute value of x.

So, we end up with:

|x|/x ... choose (5)

http://www.beatthegmat.com/if-x-0-then- ... 14328.html

Need to clarify something here. Why are we only choosing the positive square root? For Gmat purposes, isn't it INSUFFICIENT to get to an answer that contains a square root since you don't know if its the positive or the negative root, unless explicitly told in question stem if we are looking at greater than 0 or less than 0? So if we get to squareroot 25, it would be insufficient for a DS question unless say we are dealing with geometry or another question type that automatically excludes negative numbers.
Please clarify.

As for my solution, i thought it should be 1. Since if we assume that the variable is negative, then it gets cancelled out by the x in the denominator (which would now be negative), but if its positive, then the denominator is still positive and we still end up with 1.

[RonPurewal]

Need to clarify something here. Why are we only choosing the positive square root? For Gmat purposes, isn't it INSUFFICIENT to get to an answer that contains a square root since you don't know if its the positive or the negative root, unless explicitly told in question stem if we are looking at greater than 0 or less than 0?

"the square root" (and the "√" symbol) are universally described across all of mathematics -- not just the gmat -- as representing the non-negative root.

this is done so that notations are unambiguous; if this convention were not in place, then it would actually be impossible to write the positive square root of a number.
for instance, if you wanted to write the length of the diagonal of a square with side length 1, but "√2" meant either positive or negative, then how would you write that length? you wouldn't be able to.
fortunately, "√2" means only the positive square root of 2, so we are good.

[aths]

What is wrong with this...

square root of x^2/x = {(x^2)^(1/2)}/x^1

now since 2*(1/2) = 1, above equation becomes

Ans = x^1/x^1 = x^(1-1) = x^0 = 1

ANSWER = 1.

Please tell me how this is mathematically wrong....

[RonPurewal]

What is wrong with this...

square root of x^2/x = {(x^2)^(1/2)}/x^1

now since 2*(1/2) = 1, above equation becomes

Ans = x^1/x^1 = x^(1-1) = x^0 = 1

ANSWER = 1.

Please tell me how this is mathematically wrong....

the square root of x^2 is not x, it's actually |x|.

try plugging in a negative value for x and you will see exactly what is wrong.

[opp]

Hello,

For me both answer D and E hold true. If we assume X=1 => the expression equals X if we assume X=-1, the expression again equals X.

Could you please help to understand?
Thank you!
Inna

[RonPurewal]

Hello,

For me both answer D and E hold true. If we assume X=1 => the expression equals X if we assume X=-1, the expression again equals X.

Could you please help to understand?
Thank you!
Inna

Try plugging in another number that's not -1 or 1. Any other choice of x will eliminate choice (d).

[srimila]

Hi,

Simplify Sqrt (X^2)/x = x/x

But sqrt (x) = always positive

a) Hence if X is positive, sqrt (x^2)/x = positive(x)/positive (x) = positive (x/x)

b) If X is negative, sqrt (x^2)/x = positive/negative = negative (x/x).

therefore the value depends on x and the sqrt (x) = |x| and hence the answer is |x|/x.

[RonPurewal]

Hi,

Simplify Sqrt (X^2)/x = x/x

But sqrt (x) = always positive

a) Hence if X is positive, sqrt (x^2)/x = positive(x)/positive (x) = positive (x/x)

b) If X is negative, sqrt (x^2)/x = positive/negative = negative (x/x).

therefore the value depends on x and the sqrt (x) = |x| and hence the answer is |x|/x.

yeah.
for anyone to whom this doesn't instantly make sense -- just plug some specific numbers into the expression, and it will become a lot easier to see what happens and why.