Simplify √75

Step by step

The question

Question: simplify √75.

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 75.

A bigger one can't go in.

We try the biggest first.

Does 36 go into 75?

No.

Does 25 go into 75?

Yes: 75 divided by 25 is 3.

2 Split the root

So 75 is 25 times 3.

We write it under the root.

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

So √(25 × 3) is √25 times √3.

√25 is 5, because 5 times 5 is 25.

We write 5 in place of √25.

We leave out the times sign: 5√3 means 5 times √3.

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

So √75 = 5√3.

3 Check

Let's check: we square the answer.

We must get 75 back.

5 × 5, and √3 × √3 = 3.

We get 75.

So 5√3 is right!

Let's look back.

First: find the biggest square number.

Then: split the root.

Last: check.