Divide and simplify. Assume that all variables represent positive real numbers.?

Question

66 + 33√6 / 11

a. 6 + 3√6
b. 6 - 3√6
c. 9√6
d. 9√6 / 11

Answer 1

It's a little confusing whether the 11 applies to the whole sum or not. I'll assume you meant:

(66 + 33√6) / 11

Divide the individual terms by 11:
6 + 3√6

You can't add disparate terms and you can't reduce the square root further. This matches with the first answer:
A) 6 + 3√6

Answer 2

66 + 33√6 / 11
= 66/11 + 33√6 / 11
= 6 + 3√6
a. 6 + 3√6

Answer 3

it is a.