Step by step
The question
Question: simplify 4 over √8.
1 Simplify the bottom first
Simplify the bottom root first.
It keeps the numbers small.
8 is 4 times 2, and √4 is 2.
So √8 is 2√2.
So the bottom is 2√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: 4 times √2 is 4√2.
On the bottom: 2 times 2 is 4.
No root at the bottom now.
3 Cancel
4 and 4 can both be divided by 4.
4/4 is 1.
So we get √2.
4 Check
Let's check with a calculator.
The start is about 1.41.
The answer is about 1.41 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.