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 answer:

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.