1 1 a Is it true that = ? 3+ 2 1 3+ 2 3-2 3-2 Explain. b Simplify 33-2 Is the denominator rational? c Use a calculator to check that the value of your answer to part b is equal to the value of 1 3+3 The conjugate of 3 + 2 is 3-2. Find the conjugate of: a 5+23 3 b 2-3 c 5+1 The process shown in question 1 involves rationalising a surd with a binomial denominator. By first finding the conjugate of the denominator, rationalise the denominator of each expression below. 1 a 2-3 b 2 5+1 1 2 d 7 - 5+23 4 The largest cube that can fit into a sphere must have its eight vertices touching the surface of the sphere. Express the side length, s, of the cube in terms of the diameter, D, of the sphere. 5 Squares are formed inside squares by joining the midpoints of the sides of the squares as shown. If AB = 4 cm, find the exact length of the side of the shaded square. 6 Six stormwater pipes, each 2 mm in diameter, are stacked as shown in the diagram. Find the exact height, h, of this stacking. D C A B h