June 2000 Tough Nut Solution to The Root Cause Good solutions were submitted by Hyeyoun Chung, age 15, St Paul's Girls' School, London, Michal Szymanski age 16, School: Daramalan College, Ling Xiang Ning, Allan, age 13, Raffles Institution, Singapore. This is Hyeyoun's solution. We are given that is a natural number and is rational. Therefore , where x and y are integers and y 0. Then . As a is a natural number, must be a factor of . Therefore, y must be a factor of x and therefore: Therefore a is a square number. It follows that if a is not a square number then is irrational. A:\Sep00\jun00_tn396.doc 30 July, 2000