Bunuel wrote:
vhsneha wrote:
If x is positive, what is the value of \(\sqrt{x}\)
(1) \(\sqrt[3]{x}=2\)
(2) x^2=64
Comment: The official answer is D. However, since the question stem doesn't state anything about the sign of x^1/2 (only that x is positive), i am not convinced that there is a unique answer since x^1/2 can be +- 2 {(2)^1/2}
PS: I tried using the math formula buttons. Didnt work for me. Apologize for the format
If x is positive, what is the value of \(\sqrt{x}\)?(1) \(\sqrt[3]{x}=2\) --> take to the third power: x = 8 --> \(\sqrt{x}=\sqrt{8}\). Sufficient.
(2) x^2=64 --> x = 8 or x = -8. Since we are told that x is positive, then x = 8 and \(\sqrt{x}=\sqrt{8}\). Sufficient.
Answer: D.
vhsneha wrote:
Comment: The official answer is D. However, since the question stem doesn't state anything about the sign of x^1/2 (only that x is positive), i am not convinced that there is a unique answer since x^1/2 can be +- 2 {(2)^1/2}
PS: I tried using the math formula buttons. Didnt work for me. Apologize for the format
First of all, we are told that x is positive, so x cannot be \(-2\sqrt{2}\). Next, the square root cannot give a negative result, that is \(\sqrt{4}=2\) NOT +2 and -2. (In contrast the equation x^2 = 4 has TWO solutions x = 2 and x = -2).
arosman wrote:
You can't have the square root of a negative number. Irrational numbers are way beyond the scope of GMAT. If a question ask for \(\sqrt{x}\) you can assume x is positive or zero.
Yes, even roots from negative numbers are not defined for the GMAT (\(\sqrt[even]{negative}\) is undefined). So, you don't need complex numbers for the GMAT.
GMAT deals with only real numbers: integers (-3, -2, -1, 0, 1, 2, 3, ...), fractions/decimals (3/2, 4/3, 0.7, 17.5, ...) and
irrational numbers (\(\sqrt{3}\), \(\sqrt{2}\), \(\pi\), ...).
Check for more below:
2. Properties of Integers
For other subjects:
ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHey Bunuel, I still can't wrap my head around this question.
Although i DO agree that
only x can be determined to be +8 based on the stem, how can we presume that the sqrt of +8 cannot be negative?
For example, given that x = +4, then sqrt of +4 can be +/-2.
multiplying -2*-2 will return the positive x value +4.
In the case of the question - why would this not apply..?
it could effectively be written as:
\([(-\sqrt{8})^2]^(1/3)\)
EDIT: i believe the confusing part about this questions is that the question is not asking you to TAKE the square root of x, but rather assume that the expression provided is already \(\sqrt{x}\), implying that the number will always be positive.