Does a negative number have any square roots?

Answer 1

Yes, they are numbers in the complex field.

Look at it this way: You started to count with positive integers. But with only those numbers subtraction was limited. You could not take 3 from 2. The solution was to introduce negative numbers. That expanded the number system and what you could do with them.

You learned to divide, but you could not divide 2 by 3. This time the solution was to introduce [rational] fractions. Again, the number system was expanded as was the range of and its power.

You learned about square roots but even common numbers like 2 did not have a square root that was a rational number. So you introduced Irrational Numbers. Once again, the number system was expanded as was the range of and its power.

The next hurdle was the square root of negative numbers. The solution was to introduce complex numbers. And once again ... you guessed!

The introduction of each additional set of number comes as you get into more complicated areas of the subject. In the UK you will not come across complex numbers until you study further mathematics at A level.

The square roots of -9, for example, are ±3iwhere i denotes the square root of -1.