Stage: 4 and 5 Challenge Level: 
Why do this problem ?
The problem gives a neat application involving the manipulation of surds where surds occur in the denominator of a fraction.
It makes a good rounding-off to the section of work on surds which includes rationalisation of denominators.
Possible approach
This is a short problem that can be used as a lesson starter to a lesson on surds or on summing series.Key question
Can you simplify the fractions with the surds in the denominators?Weekly Challenge. Stage 5 - Core Mapping. Surds. smartphone. Stage 5 - Reviewed 2012. Individual. Powers & roots. Calculus generally. Series. Maths in STEM.
Published March 2003,April 2003.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk