How do you divide surds such as the question below?

5√20 = 5x√(4x5) = 5 x √4 x √5 = 10√5
So, "5√20 divided by 6√5" becomes "10√5 divided by 6√5" which is 10/6 or 1 2/3.

(5√20)/(6√5)
= [5√(2^2 * 5)]/(6√5)
= (5 * 2√5)/(6√5)
= (10√5)/(6√5)
= 10/6
= 5/3

5 √20
--------------
6 √5

5 x 2√5
-------------
6 √5

10
-----
6

5
----
3

√20 can be resolved as √(4*5) = √4 * √5 = 2 * √5

So, 5√20
-------
6√5

= 5 * 2 * √5
---------------
2 * 3 * √5

√5 and 2 will get canceled.

So the answer is:

5
-- or 1.667
3