Step by step
The question
Question: simplify √2 over √7.
√2√7
1 Remove the root at the bottom
A root times itself is the number inside: √7 times √7 is 7.
So we multiply the bottom by √7.
√7 × √7 = 7
To keep the fraction the same, we multiply the top by √7 too.
√7 over √7 is 1, and times 1 changes nothing.
√7√7 = 1
So we multiply by √7 over √7.
= √2√7 × √7√7
Careful!
Many people multiply only the bottom.
Then the fraction changes.
Top and bottom get the same √7.
Careful: multiply the TOP by the root too
On top: √2 times √7 is √14.
On the bottom: √7 times √7 is 7.
No root at the bottom now.
The numbers can't be cancelled, so we are done.
= √147
2 Check
Let's check with a calculator.
The start is about 0.53.
Start: √2√7 ≈ 0.53
The answer is about 0.53 too.
So it is right!
Answer: √147 ≈ 0.53
Let's look back.
First: remove the root at the bottom.
Last: check.
Answer
= √147