Simplify √48

Step by step

The question

Question: simplify √48.

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 48.

A bigger one can't go in.

We try the biggest first.

Does 16 go into 48?

Yes: 48 divided by 16 is 3.

2 Split the root

So 48 is 16 times 3.

We write it under the root.

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

So √(16 × 3) is √16 times √3.

√16 is 4, because 4 times 4 is 16.

We write 4 in place of √16.

We leave out the times sign: 4√3 means 4 times √3.

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

So √48 = 4√3.

3 Check

Let's check: we square the answer.

We must get 48 back.

4 × 4, and √3 × √3 = 3.

We get 48.

So 4√3 is right!

Let's look back.

First: find the biggest square number.

Then: split the root.

Last: check.