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

Question

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.

mygmat0101 · Answer

Here's my 2 cents

From What I have known, GMAT only considers positive roots.

Bunuel · Answer

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 {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 .

PrernaMurada · Answer

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

ccooley · Answer

This article lays out the whole situation: https://www.manhattanprep.com/gmat/blog ... -the-gmat/

danielarasan · Answer

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

vikas304 · Answer

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

This means x can be - 11},\sqrt{11}

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

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