Review question

# Can we find an approximation to $\sqrt{5}+\sqrt{3}$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7477

## Question

If $\dfrac{b}{a}$ is small enough for powers of $\dfrac{b}{a}$ higher than the third to be neglected, show that $\begin{equation*} (a+b)^\frac{1}{2} - (a-b)^\frac{1}{2} = a^\frac{1}{2} \left( \frac{b}{a} + \frac{b^3}{8a^3} \right). \end{equation*}$

Use this result to deduce a rational approximation to $\sqrt 5 - \sqrt 3$.

Deduce, or obtain otherwise, a rational approximation to $\sqrt 5 + \sqrt 3$.