Find the exact length of side A in the triangle and give you answer in the simplest form. (It is a right angled triangle. Side C is (6+√(3)) and side B is (3 + 2√(3)).

a² + b² = c²    (Pythagoras' Theorem) 

a² + (3 + 2√(3))(3 + 2√(3)) = (6 + √(3))(6 + √(3))    (Expanding brackets)

a² + 9 + 6√(3) + 6√(3) + 12 = 36 + 6√(3) + 6√(3) + 3   (Multiplying and simplifying surds)

a² + 21 + 12√(3) = 39 + 12√(3)    (Solving quadratic equations)

a² = 39 - 21 = 18

a = √(2) x √(9)    (Simplifying answer as requested in question)

a = 3√(2)