Higher June 2018 Paper 1 Q28
28 Simplify \(\quad \sqrt{80} + \sqrt{2\dfrac{2}{9}}\)
Give your answer in the form \(\quad \dfrac{a\sqrt{5}}{b} \quad\) where \(a\) and \(b\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{14\sqrt{5}}{3}\) | B3 | oe eg \(\dfrac{28\sqrt{5}}{6}\) B2 (\(\sqrt{2\frac{2}{9}} =\)) \(\dfrac{2\sqrt{5}}{3}\) or (\(\sqrt{80} =\)) \(4\sqrt{5}\) and (\(\sqrt{2\frac{2}{9}} =\)) \(\dfrac{\sqrt{20}}{3}\) or (\(\sqrt{2\frac{2}{9}} =\)) \(\dfrac{2\sqrt{5}}{\sqrt{9}}\) B1 (\(\sqrt{80} =\)) \(4\sqrt{5}\) or (\(\sqrt{2\frac{2}{9}} =\)) \(\dfrac{\sqrt{20}}{3}\) or (\(\sqrt{2\frac{2}{9}} =\)) \(\dfrac{2\sqrt{5}}{\sqrt{9}}\) |
Additional guidance
| For B1 or B2, allow \(\dfrac{6\sqrt{5}}{9}\) for \(\dfrac{2\sqrt{5}}{3}\) and \(\dfrac{\sqrt{180}}{9}\) for \(\dfrac{\sqrt{20}}{3}\) | |
| \(\dfrac{14}{3}\sqrt{5}\) | B3 |
| \(16\sqrt{5} + \dfrac{2\sqrt{5}}{3} = \dfrac{50\sqrt{5}}{3}\) | B2 |
| \(4\sqrt{5} + \dfrac{2\sqrt{5}}{3} = 4\dfrac{2}{3}\sqrt{5}\) | B2 |
| \(4\sqrt{5} + \dfrac{2\sqrt{5}}{9} = \dfrac{38\sqrt{5}}{9}\) | B1 |
| \(2\sqrt{20} + \dfrac{\sqrt{20}}{3} = \dfrac{7\sqrt{20}}{3}\) | B1 |