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
80 = 24
5
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