Step by step
The question
Question: simplify 12 over √6.
12√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.
√6 × √6 = 6
To keep the fraction the same, we multiply the top by √6 too.
√6 over √6 is 1, and times 1 changes nothing.
√6√6 = 1
So we multiply by √6 over √6.
= 12√6 × √6√6
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √6.
Careful: multiply the TOP by the root too
On top: 12 times √6 is 12√6.
On the bottom: √6 times √6 is 6.
No root at the bottom now.
= 12√66
2 Cancel
12 and 6 can both be divided by 6.
12/6 is 2.
12 ÷ 6 = 2, 6 ÷ 6 = 1
So we get 2√6.
= 2√6
3 Check
Let's check with a calculator.
The start is about 4.90.
Start: 12√6 ≈ 4.90
The answer is about 4.90 too.
So it is right!
Answer: 2√6 ≈ 4.90
Let's look back.
First: remove the root at the bottom.
Then: cancel.
Last: check.
Answer
= 2√6