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# x^2 = 11, then x = root of 11 . Is this statement true or false

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Manager
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Joined: 03 Jul 2017
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x^2 = 11, then x = root of 11 . Is this statement true or false  [#permalink]

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05 Feb 2018, 07:19
If x^2 = 11, then x = root of 11 . Is this statement true or false

Now my doubt is that how can x be a root of -11??
Can someone explain because to my understanding the root of a number cannot be negative.
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Joined: 04 Jan 2018
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false  [#permalink]

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05 Feb 2018, 07:27
Here's my 2 cents

From What I have known, GMAT only considers positive roots.
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x^2 = 11, then x = root of 11 . Is this statement true or false  [#permalink]

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05 Feb 2018, 07:35
longhaul123 wrote:
If x^2 = 11, then x = root of 11 . Is this statement true or false

Now my doubt is that how can x be a root of -11??
Can someone explain because to my understanding the root of a number cannot be negative.

If x^2 = 11, then $$x = \sqrt{11}$$ or $$x = -\sqrt{11}$$

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

$$\sqrt{9} = 3$$, NOT +3 or -3;
$$\sqrt[4]{16} = 2$$, NOT +2 or -2;

Notice that in contrast, the equation $$x^2 = 9$$ has TWO solutions, +3 and -3. Because $$x^2 = 9$$ means that $$x =-\sqrt{9}=-3$$ or $$x=\sqrt{9}=3$$.
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false  [#permalink]

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10 Feb 2018, 05:12
If x^2 = 11, then x=11^0.5 or x=-11^0.5

But if you are solving x=9^0.5,then x is only 3.
Because square root of a Positive real number is always positive
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false  [#permalink]

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19 Feb 2018, 10:01
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false  [#permalink]

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24 Feb 2018, 10:43
The best way to approach this kind of problem is to isolate Zero

For example:
X^2 = 11, should be x^2 - 11 = 0
Then you do the difference of squares:
(x+ √11) (x - √11) = 0
In this case, x = -√11 or x =√11

Regarding your question, -√11 is possible on the GMAT. It is the negative of √11, something close to - 3.3

As others mentioned, if the question asked something like what is √11, then ˜3.3 would be the only answer
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false  [#permalink]

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09 May 2018, 10:35

False, I would say! Because x^2 = 11, you can convert it to equation (x-\sqrt{11[square_root])(x+[square_root]11[square_root]) = 0

This means x can be -[square_root]11},\sqrt{11}
Re: x^2 = 11, then x = root of 11 . Is this statement true or false   [#permalink] 09 May 2018, 10:35
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