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

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longhaul123
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x^2 = 11, then x = root of 11 . Is this statement true or false [#permalink] New post   05 Feb 2018, 08:19
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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mygmat0101
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false [#permalink] New post   05 Feb 2018, 08:27
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] New post   05 Feb 2018, 08:35
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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] New post   10 Feb 2018, 06:12
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] New post   19 Feb 2018, 11:01
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This article lays out the whole situation: https://www.manhattanprep.com/gmat/blog ... -the-gmat/
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danielarasan
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false [#permalink] New post   24 Feb 2018, 11:43
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] New post   09 May 2018, 11:35


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}
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Re: x^2 = 11, then x = root of 11 . Is this statement true or false [#permalink]
09 May 2018, 11:35
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