Exercise 46 Page 626

Let's begin with recalling the definition of the geometric mean. The geometric mean of two positive numbers aand bis the numberxsuch thatx=sqrt(a* b). In our exercise, we are asked to determine if the geometric mean for two perfect squares is a positive integer. To do this, let's assume that m and n are integers and evaluate the geometric mean for their squares. Since the product of two positive integers is always a positive integer, we can say that the geometric mean for two perfect squares is always a positive integer.