Quandaries
and Queries 

Hi there, if I am given any number (say 80 for example), how may I determine the smallest whole number integer which when multipled by it will yield a square number ? In other words if I express this as: 80 * n = square number, what is the least value of n which will yield a square. Best Regards secondary level student 

Hi, First find the prime decomposition of 80
If an integer is a square then, in its prime decomposition, each prime must be raised to an even power. In this example 2 is raised to an even power but 5 is not. Thus the smallest whole number n that makes 80 n a square is n = 5. Penny 

