Surds (Edexcel IGCSE Further Pure Maths): Exam Questions

Expand $\frac{3}{\sqrt{1-2x}}$ in ascending powers of $x$ up to and including the term in $x^3$

and simplifying each term as far as possible.

Write down the range of values of $x$ for which this expansion is valid.

Show that $\frac{3}{\sqrt{0.9}}=\sqrt{10}$

Express $\frac{1}{\sqrt{10}-3}$ in the form $a\sqrt{10}+b$ , where $a$ and $b$ are integers.

Hence, using your expansion with a suitable value for $x$, obtain an approximation to $5$ decimal places of $\frac{1}{\sqrt{10}-3}$