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)
