Simplify √72

Step by step

The question

Question: simplify √72.

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 72.

A bigger one can't go in.

We try the biggest first.

Does 36 go into 72?

Yes: 72 divided by 36 is 2.

2 Split the root

So 72 is 36 times 2.

We write it under the root.

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

So √(36 × 2) is √36 times √2.

√36 is 6, because 6 times 6 is 36.

We write 6 in place of √36.

We leave out the times sign: 6√2 means 6 times √2.

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

So √72 = 6√2.

3 Check

Let's check: we square the answer.

We must get 72 back.

6 × 6, and √2 × √2 = 2.

We get 72.

So 6√2 is right!

Let's look back.

First: find the biggest square number.

Then: split the root.

Last: check.