Show that 12 cos 30° - 2 tan 60° can be written in the form root (k) where k is an integer.

To answer these questions, students must know the values of cos30 and tan60. If you don't know them off by heart, you can work them out using an equilateral triangle.

cos 30° = adj / hyp = root(3) / 2

tan 60° = opp / adj = root(3) / 1 = root(3)

Once we know these values we can plug them into the original expression and find that it can be written as root(48). Careful, 4root(3) is not the right answer and you'll lose some marks, because the question does not ask for an integer at the front. To sidestep this, we have to do a bit more work. Rewrite 4 as root(16), and then know that roots can be multiplied together (16 x 3 = 48)

Therefore, => 12(root(3) / 2) - 2(root(3)) = 6root(3) - 2root(3) = 4root(3) 4root(3) = root(16) x root(3) = root(48) Therefore k = 48