What is square root 10 over square root 3 in simplest radical form

I'll give you a few examples of a square root over a square root first, so you'll understand how I got the

1. √a / √b = √ab / b
2. √2 / √3 = √2*3 / 3 = √6 / 3
3. 1 / √a = √a / a
4. √3 / √7 = √21 / 7

I think you get how it works now.

Now lets solve the question.

√10 / √3 
can also be written as √10 * 1/√3
1/√3 simplified is √3/3
So, √10 / √3 = √10 * √3/3
= √10*√3 / 3
= √30 / 3
Factor 30 (2*3*5) and make sure there are no pairs of factors that are the same. (for example: two 2's or two 4's)
If there are any pairs of factors, then take them outside the square root.
ex: √20 = √2*2*5 = 2√5

That was the long way to solve it, but there is a trick:
Remember what √a / √b equals?
It equals √a*b / b.
This means √10 / √3 is simply just √30 / 3.
Then all you need to do is make sure the number inside the radical has no pairs of factors then you are good to go.