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:
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