Step by step
The question
Question: simplify 10 over √5.
10√5
1 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.
√5 × √5 = 5
To keep the fraction the same, we multiply the top by √5 too.
√5 over √5 is 1, and times 1 changes nothing.
√5√5 = 1
So we multiply by √5 over √5.
= 10√5 × √5√5
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √5.
Careful: multiply the TOP by the root too
On top: 10 times √5 is 10√5.
On the bottom: √5 times √5 is 5.
No root at the bottom now.
= 10√55
2 Cancel
10 and 5 can both be divided by 5.
10/5 is 2.
10 ÷ 5 = 2, 5 ÷ 5 = 1
So we get 2√5.
= 2√5
3 Check
Let's check with a calculator.
The start is about 4.47.
Start: 10√5 ≈ 4.47
The answer is about 4.47 too.
So it is right!
Answer: 2√5 ≈ 4.47
Let's look back.
First: remove the root at the bottom.
Then: cancel.
Last: check.
Answer
= 2√5