What is the square root of -2?
The answer your teacher will give depends on where you are in you mathematics education.
There is no positive or negative number that is the square root of
If we square a positive number we get a positive answer.
If we square a negative number, we still get a positive number.
There is no positive or negative number (real number) whose square is negative.
We know that, for positive numbers
Following the same reasoning we would expect to have:
There is a problem with
The solution is to invent a new number whose square is
Using tis new number, we can write
But, if we want to keep our usual arithmetic, then
But we also have
Because it is a bother to write and say
(In mathematics. we call it
The square root symbol means the one without a minus sign in front, so