Simplify √200

Step by step

The question

Question: simplify √200.

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 200.

A bigger one can't go in.

We try the biggest first.

Does 100 go into 200?

Yes: 200 divided by 100 is 2.

2 Split the root

So 200 is 100 times 2.

We write it under the root.

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

So √(100 × 2) is √100 times √2.

√100 is 10, because 10 times 10 is 100.

We write 10 in place of √100.

We leave out the times sign: 10√2 means 10 times √2.

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

So √200 = 10√2.

3 Check

Let's check: we square the answer.

We must get 200 back.

10 × 10, and √2 × √2 = 2.

We get 200.

So 10√2 is right!

Let's look back.

First: find the biggest square number.

Then: split the root.

Last: check.