Step by step
The question
Question: simplify 10 over √20.
1 Simplify the bottom first
Simplify the bottom root first.
It keeps the numbers small.
20 is 4 times 5, and √4 is 2.
So √20 is 2√5.
So the bottom is 2√5.
2 Remove the root at the bottom
A root times itself is the number inside: √5 times √5 is 5.
So we multiply the bottom by √5.
To keep the fraction the same, we multiply the top by √5 too.
√5 over √5 is 1, and times 1 changes nothing.
So we multiply by √5 over √5.
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √5.
On top: 10 times √5 is 10√5.
On the bottom: 2 times 5 is 10.
No root at the bottom now.
3 Cancel
10 and 10 can both be divided by 10.
10/10 is 1.
So we get √5.
4 Check
Let's check with a calculator.
The start is about 2.24.
The answer is about 2.24 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.