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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

Re: If x is positive, what is the value of x^(1/2)?
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18 May 2018, 18:33

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1

If x is positive, what is the value of sqrt x

(1) (x^1/3)=2 (2) x^2=64

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.
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Re: If x is positive, what is the value of x^(1/2)?
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18 May 2018, 18:45

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1

I agree. And I am considering x to be positive (8). However the question asks for sqrt of x. It doesn't suggest that sqrt of x is positive. hence it can be +- 2(2)^1/2. Am I missing something?

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18 May 2018, 18:46

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vhsneha wrote:

If x is positive, what is the value of sqrt x

(1) (x^1/3)=2 (2) x^2=64

In GMAT, we only consider the +ve root value of a square root. Example: x= \(\sqrt{4}\) -> x=2, whereas \(x^2\) = 4 -> x =+2 0r -2.

Now coming to the question, as we are asked about \(\sqrt{x}\).

St1: \(x^\frac{1}{3}\)=2 -> x=\(2^3\) so, \(\sqrt{x}\) = \(\sqrt{2^3}\). We can definitely get the value of x. Sufficient.

St2: \(x^2\)=64 -> x=+8 0r -8. Note: We cannot have square root of a -ve number so, \(\sqrt{x}\) = \(\sqrt{8}\). We can definitely get the value of x. Sufficient.

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18 May 2018, 18:52

When the GMAT gives you a square root symbol, it’s referring to one specific value: the positive square root.

So from statement 1: x=2^3=8. Sufficient. Statement 2: x^2=64 IxI=8; x can be +8 or,-8. As per question stem x is positive. So only x=8 satisfied. Hence sufficient

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 (\(\sqrt{3}\), \(\sqrt{2}\), \(\pi\), ...).

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15 Dec 2019, 06:12

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