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# If x is positive, what is the value of x^(1/2)?

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If x is positive, what is the value of x^(1/2)?  [#permalink]

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Updated on: 18 May 2018, 23:28
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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

Originally posted by vhsneha on 18 May 2018, 18:25.
Last edited by Bunuel on 18 May 2018, 23:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x is positive, what is the value of x^(1/2)?  [#permalink]

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18 May 2018, 18:33
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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)?  [#permalink]

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

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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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Re: If x is positive, what is the value of x^(1/2)?  [#permalink]

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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

Ans: D

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Re: If x is positive, what is the value of x^(1/2)?  [#permalink]

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19 May 2018, 00:05
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.

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 ! ! !
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Re: If x is positive, what is the value of x^(1/2)?  [#permalink]

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15 Dec 2019, 06:12
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Re: If x is positive, what is the value of x^(1/2)?   [#permalink] 15 Dec 2019, 06:12