Moderate -0.8 This is a straightforward surds manipulation question requiring simplification of square roots and rationalizing the denominator. While it involves multiple steps (simplifying √32 and √18, combining like terms, then rationalizing), these are all standard techniques with no problem-solving insight required. The 5 marks reflect the working steps rather than conceptual difficulty, making this easier than average.
In this question you should show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Simplify
$$\frac{\sqrt{32} + \sqrt{18}}{3 + \sqrt{2}}$$
giving your answer in the form \(b\sqrt{2} + c\), where \(b\) and \(c\) are integers. [5]
In this question you should show all stages of your working.
Solutions relying on calculator technology are not acceptable.
Simplify
$$\frac{\sqrt{32} + \sqrt{18}}{3 + \sqrt{2}}$$
giving your answer in the form $b\sqrt{2} + c$, where $b$ and $c$ are integers. [5]
\hfill \mbox{\textit{SPS SPS SM 2022 Q3 [5]}}