To simplify the expression √(36-12√5) : √6, we can start by simplifying the numerator and denominator separately.

√(36-12√5) can be simplified as follows:
Let's assume √(36-12√5) = a + b√5, where a and b are real numbers.
Squaring both sides, we get:
36-12√5 = a^2 + 2ab√5 + 5b^2

From this equation, we can equate the real and imaginary parts:
36 = a^2 + 5b^2 ----(1)
-12√5 = 2ab√5 ----(2)

From equation (2), we can simplify it to:
-6 = ab

Substituting this value of ab in equation (1), we get:
36 = a^2 + 5(-6/a)^2
36 = a^2 + 5(36/a^2)
36 = a^2 + 180/a^2
Multiplying through by a^2, we get:
36a^2 = a^4 + 180
Rearranging the equation, we get:
a^4 - 36a^2 + 180 = 0

This is a quadratic equation in terms of a^2. Solving this equation, we find that a^2 = 18 ± 6√5.

Taking the positive value, a^2 = 18 + 6√5.
Taking the square root of both sides, we get:
a = √(18 + 6√5)

Now, substituting the value of a in equation (2), we get:
-6 = √(18 + 6√5) * b
Squaring both sides, we get:
36 = (18 + 6√5) * b^2
Dividing through by (18 + 6√5), we get:
b^2 = 2 - √5
Taking the square root of both sides, we get:
b = √(2 - √5)

Therefore, √(36-12√5) = √(18 + 6√5) + √(2 - √5)

Now, let's simplify the denominator, √6:
√6 = √(2 * 3) = √2 * √3 = √2√3 = √(2√3)

Now, we can rewrite the expression as:
(√(18 + 6√5) + √(2 - √5)) : √(2√3)

This is the simplified form of the expression.