Step by step
The question
Question: simplify 6 over √3.
6√3
1 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.
√3 × √3 = 3
To keep the fraction the same, we multiply the top by √3 too.
√3 over √3 is 1, and times 1 changes nothing.
√3√3 = 1
So we multiply by √3 over √3.
= 6√3 × √3√3
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √3.
Careful: multiply the TOP by the root too
On top: 6 times √3 is 6√3.
On the bottom: √3 times √3 is 3.
No root at the bottom now.
= 6√33
2 Cancel
6 and 3 can both be divided by 3.
6/3 is 2.
6 ÷ 3 = 2, 3 ÷ 3 = 1
So we get 2√3.
= 2√3
3 Check
Let's check with a calculator.
The start is about 3.46.
Start: 6√3 ≈ 3.46
The answer is about 3.46 too.
So it is right!
Answer: 2√3 ≈ 3.46
Let's look back.
First: remove the root at the bottom.
Then: cancel.
Last: check.
Answer
= 2√3