Review question

# Can we find a good rational approximation for $\sqrt{5}$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6340

## Suggestion

Prove that, if $x$ is so small that its cube and higher powers can be neglected, $\sqrt{\frac{1+x}{1-x}} = 1 + x + \frac{x^2}{2}.$ By taking $x = \dfrac{1}{9}$, prove that $\sqrt{5}$ is approximately equal to $\dfrac{181}{81}$.

Can we rewrite the left-hand side as a product of functions that we do know how to expand?