Review question

# Can we prove these bounds for this fraction involving surds? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7077

## Suggestion

1. Express $\frac{\sqrt{a}+\sqrt{b}}{\sqrt{a}-\sqrt{b}}$ as a fraction having a rational denominator.

The question asks us to get rid of the square roots in the denominator; what method might we use?

Can we multiply $\sqrt{a}-\sqrt{b}$ by something so that we lose the square roots?

1. Show that, if $n$ is a positive integer, then $n(n+2)$ lies between $n^2$ and $(n+1)^2$.

What is $n(n+2) - (n+1)^2$?

1. If $n$ is a positive integer, use the results in (i) and (ii) to find in terms of $n$ two consecutive integers between which $\frac{\sqrt{n+2}+\sqrt{n}}{\sqrt{n+2}-\sqrt{n}}$ must lie.

The question tells us to use results we’ve already proved… like many exam questions!