4MA0 Higher January 2012 Paper 3 Q19
19 Show that \(\dfrac{\sqrt{3} + \sqrt{27}}{\sqrt{2}}\) can be expressed in the form \(\sqrt{k}\) where \(k\) is an integer.
State the value of \(k\).
(3)
| Scheme | Marks |
|---|---|
| \((\sqrt{3} + 3\sqrt{3})/\sqrt{2}\) | M1 |
\(4\sqrt{3}/\sqrt{2}\) \(2\sqrt{6}\) or \((\sqrt{48}/\sqrt{2})\) | M1 |
| 24 | A1cao |
| (Total 3 marks) |
Notes
M1: Must see \(\sqrt{27}\) reduce to \(3\sqrt{3}\) alternative \(\dfrac{\sqrt{6} + \sqrt{54}}{2}\) (or better)
M1: dep on 1st M1
A1cao: dep on M2 Accept \(\sqrt{24}\) if M2 awarded.