^{(1/2)}= √(-1).

To get around this problem we can just make up an answer. We'll call this answer

*i*. It can't be a real number, so it is outside the real numbers.

Using

*i*allows us to find roots for all negative numbers. For example

√(-2) = √(2 × -1) = √2 × √(-1)= (√2)

*i*= 1.414

*i*

Both negative and positive numbers have two square roots. Just as both 4

^{2}and (-4)

^{2}are 16, both (4

*i*)

^{2}and (-4

*i*)

^{2}are -16.

When we look at cube roots, thing get more complicated. Now every number has three cube roots, not just one, like it did with the real numbers. So not only does 3

^{3}equal 27, but so does (-3/2 + (3√3/2)

*i*)

^{3}and (-3/2 + (3√3/2)

*i*)

^{3}

For more on this see the complex numbers.

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