Simplify √18

Step by step

The question

Question: simplify √18.

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 18.

A bigger one can't go in.

We try the biggest first.

Does 9 go into 18?

Yes: 18 divided by 9 is 2.

2 Split the root

So 18 is 9 times 2.

We write it under the root.

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

So √(9 × 2) is √9 times √2.

√9 is 3, because 3 times 3 is 9.

We write 3 in place of √9.

We leave out the times sign: 3√2 means 3 times √2.

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

So √18 = 3√2.

3 Check

Let's check: we square the answer.

We must get 18 back.

3 × 3, and √2 × √2 = 2.

We get 18.

So 3√2 is right!

Let's look back.

First: find the biggest square number.

Then: split the root.

Last: check.