# What is the square root of -2?

##### 1 Answer

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.**

But,

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