Prove that if a is a natural number and the square root of a is
rational, then it is a square number (an integer n^2 for some
Stage: 5 Challenge Level:
A generalisation of the simple application of mathematical
induction is used here. You have to consider an odd number of
people and increase or decrease the number in twos. You also have
to think when 'having a not so secure foothold up the ladder' how
to look down to the previous stage then use the hypothesis to
secure that higher foothold.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.