Step by step
The question
Question: simplify 3 over √18.
1 Simplify the bottom first
Simplify the bottom root first.
It keeps the numbers small.
18 is 9 times 2, and √9 is 3.
So √18 is 3√2.
So the bottom is 3√2.
2 Remove the root at the bottom
A root times itself is the number inside: √2 times √2 is 2.
So we multiply the bottom by √2.
To keep the fraction the same, we multiply the top by √2 too.
√2 over √2 is 1, and times 1 changes nothing.
So we multiply by √2 over √2.
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √2.
On top: 3 times √2 is 3√2.
On the bottom: 3 times 2 is 6.
No root at the bottom now.
3 Cancel
3 and 6 can both be divided by 3.
3/6 is 1/2.
So we get √2/2.
4 Check
Let's check with a calculator.
The start is about 0.71.
The answer is about 0.71 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.