Step by step
The question
Question: simplify √300.
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 300.
A bigger one can't go in.
We try the biggest first.
Does 144 go into 300?
No.
Does 121 go into 300?
No.
Does 100 go into 300?
Yes: 300 divided by 100 is 3.
2 Split the root
So 300 is 100 times 3.
We write it under the root.
Rule: a root over a times can be split into two roots.
So √(100 × 3) is √100 times √3.
√100 is 10, because 10 times 10 is 100.
We write 10 in place of √100.
We leave out the times sign: 10√3 means 10 times √3.
3 has no square number in it, so we are done.
So √300 = 10√3.
3 Check
Let's check: we square the answer.
We must get 300 back.
10 × 10, and √3 × √3 = 3.
We get 300.
So 10√3 is right!
Let's look back.
First: find the biggest square number.
Then: split the root.
Last: check.