Step by step
The question
Question: simplify 2√12.
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 12.
A bigger one can't go in.
We try the biggest first.
Does 4 go into 12?
Yes: 12 divided by 4 is 3.
2 Split the root
So 12 is 4 times 3.
We write it under the root.
2√12 means 2 times √12.
Rule: a root over a times can be split into two roots.
So √(4 × 3) is √4 times √3.
√4 is 2, because 2 times 2 is 4.
We write 2 in place of √4.
2 times 2 is 4.
We leave out the times sign: 4√3 means 4 times √3.
3 has no square number in it, so we are done.
So 2√12 = 4√3.
3 Check
Let's check: we square both.
They must give the same number.
Squared means times itself.
First the start: 2 × 2, and √12 × √12 = 12.
Now the answer: 4 × 4, and √3 × √3 = 3.
Both give 48.
So 4√3 is right!
Let's look back.
First: find the biggest square number.
Then: split the root.
Last: check.