Answer:
See below.
Step-by-step explanation:
Since sqrt(a) and sqrt(b) are in simplest radical form, that means a and b have no perfect square factors. When sqrt(a) and sqrt(b) are multiplied giving c * sqrt(d), the fact that c came out of the root means that there was c^2 inside the product sqrt(ab). This means that a and b have at least one common factor.
ab = c^2d
Example:
Let a = 6 and let b = 10.
sqrt(6) and sqrt(10) are in simplest radical form.
Now we multiply the radicals.
sqrt(a) * sqrt(b) = sqrt(6) * sqrt(10) = sqrt(60) = sqrt(4 * 15) = 2sqrt(15)
We have c = 2 and d = 15.
ab = c^2d
6 * 10 = 2^2 * 15
60 = 60
Our relationship between a, b and c, d works.
