Step by step
The question
Question: simplify 9√2 over √6.
1 Remove the root at the bottom
A root times itself is the number inside: √6 times √6 is 6.
So we multiply the bottom by √6.
To keep the fraction the same, we multiply the top by √6 too.
√6 over √6 is 1, and times 1 changes nothing.
So we multiply by √6 over √6.
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √6.
On top: 9√2 times √6 is 9√12.
On the bottom: √6 times √6 is 6.
No root at the bottom now.
2 Simplify the root
Now we make √12 simpler, like in the lesson on square roots.
The biggest square that goes into 12 is 4: 12 divided by 4 is 3.
So √12 is √4 times √3.
√4 is 2, because 2 times 2 is 4.
9 times 2 is 18.
So we get 18√3.
3 Cancel
18 and 6 can both be divided by 6.
18/6 is 3.
So we get 3√3.
4 Check
Let's check with a calculator.
The start is about 5.20.
The answer is about 5.20 too.
So it is right!
Let's look back.
First: remove the root at the bottom.
Then: simplify the root.
Then: cancel.
Last: check.