Simplify √98

Step by step

The question

Question: simplify √98.

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 98.

A bigger one can't go in.

We try the biggest first.

Does 49 go into 98?

Yes: 98 divided by 49 is 2.

2 Split the root

So 98 is 49 times 2.

We write it under the root.

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

So √(49 × 2) is √49 times √2.

√49 is 7, because 7 times 7 is 49.

We write 7 in place of √49.

We leave out the times sign: 7√2 means 7 times √2.

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

So √98 = 7√2.

3 Check

Let's check: we square the answer.

We must get 98 back.

7 × 7, and √2 × √2 = 2.

We get 98.

So 7√2 is right!

Let's look back.

First: find the biggest square number.

Then: split the root.

Last: check.