Step by step
The question
Question: simplify 5 over √10.
5√10
1 Remove the root at the bottom
A root times itself is the number inside: √10 times √10 is 10.
So we multiply the bottom by √10.
√10 × √10 = 10
To keep the fraction the same, we multiply the top by √10 too.
√10 over √10 is 1, and times 1 changes nothing.
√10√10 = 1
So we multiply by √10 over √10.
= 5√10 × √10√10
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √10.
Careful: multiply the TOP by the root too
On top: 5 times √10 is 5√10.
On the bottom: √10 times √10 is 10.
No root at the bottom now.
= 5√1010
2 Cancel
5 and 10 can both be divided by 5.
5/10 is 1/2.
5 ÷ 5 = 1, 10 ÷ 5 = 2
So we get √10/2.
= √102
3 Check
Let's check with a calculator.
The start is about 1.58.
Start: 5√10 ≈ 1.58
The answer is about 1.58 too.
So it is right!
Answer: √102 ≈ 1.58
Let's look back.
First: remove the root at the bottom.
Then: cancel.
Last: check.
Answer
= √102