Simplify √8

Step by step

The question

Question: simplify √8.

1 Find the biggest square number

Square numbers are a number times itself: 2 × 2 = 4, 3 × 3 = 9, and so on.

We list them up to half of 8.

A bigger one can't go in.

We try the biggest first.

Does 4 go into 8?

Yes: 8 divided by 4 is 2.

2 Split the root

So 8 is 4 times 2.

We write it under the root.

Rule: a root over a times can be split into two roots.

So √(4 × 2) is √4 times √2.

√4 is 2, because 2 times 2 is 4.

We write 2 in place of √4.

We leave out the times sign: 2√2 means 2 times √2.

2 has no square number in it, so we are done.

So √8 = 2√2.

3 Check

Let's check: we square the answer.

We must get 8 back.

2 × 2, and √2 × √2 = 2.

We get 8.

So 2√2 is right!

Let's look back.

First: find the biggest square number.

Then: split the root.

Last: check.