Help!

[aanchalsinha]

If x=√64, and y=x+8, y may be which of the following?
I) 0
II) 8
III) 16

My soln:
√64 = √8^2 = |8|

therefore, y = |8| + 8 = 0 or 16

however, the answer is III) only.

[jnelson0612]

When the GMAT asks you to take the square root of a particular number, the result is always the positive root only. This confuses students, so let me give you an example:

If x^2=25, then x could be 5 or -5.

However, the square root of 25 is positive 5 only.

Hope this helps!

[aanchalsinha]

Thanks a lot for your response. So I recently came across a question on the GMAT Prep which also in my view tests the same concept.

sqrt(x^2)/x = ?

the answer is |x|/x

Does this mean the rule that sqrt of a number always equals the +ve root is applicable to numbers only and not variables?

Thanks

[jnelson0612]

Thanks a lot for your response. So I recently came across a question on the GMAT Prep which also in my view tests the same concept.

sqrt(x^2)/x = ?

the answer is |x|/x

Does this mean the rule that sqrt of a number always equals the +ve root is applicable to numbers only and not variables?

Thanks

No, this problem reflects the rule nicely.

For instance, is we plug in -2 for x, we get:

sqrt4/-2 which would be 2/-2. Notice that we HAVE to have a positive number in the numerator since we are taking the square root of a positive number. However, our x may be positive or negative. Taking the absolute value of x ensures that we obtain a positive number on top.

[baglobalassociates]

Yes I like these type of questions.

Thanks you

[jnelson0612]

You are welcome!

[aanchalsinha]

Thanks jnelson! absolutes confuse me sometimes :)

[jnelson0612]

Me too! They are confusing! :-)