Simplify √(-12)

Step by step

The question

Question: simplify √(−12).

No real number times itself is negative.

So we use a new number: i, the square root of minus 1.

So i squared is minus 1.

1 Split off the minus

−12 is 12 times minus 1.

We split the root: the root of 12, times the root of minus 1.

We split only to take out the minus 1.

2 Use i

12 is 4 times 3.

The square root of 4 is 2.

So the square root of 12 is 2√3.

And √(−1) is i.

We write the i before the square root, so it is clearly not under it.

So √(−12) is 2i√3.

Let's look back.

First: split off the minus.

Last: use i.