Step by step
The question
Question: simplify 6 over √12.
1 Simplify the bottom first
Simplify the bottom root first.
It keeps the numbers small.
12 is 4 times 3, and √4 is 2.
So √12 is 2√3.
So the bottom is 2√3.
2 Remove the root at the bottom
A root times itself is the number inside: √3 times √3 is 3.
So we multiply the bottom by √3.
To keep the fraction the same, we multiply the top by √3 too.
√3 over √3 is 1, and times 1 changes nothing.
So we multiply by √3 over √3.
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √3.
On top: 6 times √3 is 6√3.
On the bottom: 2 times 3 is 6.
No root at the bottom now.
3 Cancel
6 and 6 can both be divided by 6.
6/6 is 1.
So we get √3.
4 Check
Let's check with a calculator.
The start is about 1.73.
The answer is about 1.73 too.
So it is right!
Let's look back.
First: simplify the bottom first.
Then: remove the root at the bottom.
Then: cancel.
Last: check.