To simplify the expression C = √(1-√3)² - √3, we can start by simplifying the term inside the square root.

(1-√3)² = (1-√3)(1-√3)
= 1 - √3 - √3 + (√3)²
= 1 - 2√3 + 3
= 4 - 2√3

Now we can substitute this value back into the original expression:

C = √(4 - 2√3) - √3

Since we cannot simplify this expression any further, this is the final answer.