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



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.



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