Simplify √(-25)

Step by step

The question

Question: simplify √(−25).

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

−25 is 25 times minus 1.

We split the root: the root of 25, times the root of minus 1.

We split only to take out the minus 1.

2 Use i

The square root of 25 is the positive number that times itself makes 25.

5 times 5 is 25.

And the square root of minus 1 is i.

So √(−25) is 5i.

3 Check

Let's check: square the answer.

5 squared is 25, and i squared is minus 1.

We get −25.

Let's look back.

First: split off the minus.

Then: use i.

Last: check.