Simplify √(-16)

Step by step

The question

Question: simplify √(−16).

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

−16 is 16 times minus 1.

We split the root: the root of 16, times the root of minus 1.

We split only to take out the minus 1.

2 Use i

The square root of 16 is the positive number that times itself makes 16.

4 times 4 is 16.

And the square root of minus 1 is i.

So √(−16) is 4i.

3 Check

Let's check: square the answer.

4 squared is 16, and i squared is minus 1.

We get −16.

Let's look back.

First: split off the minus.

Then: use i.

Last: check.