Final answer:
To find the least positive integer b > 40 such that H(40,b) is also a positive integer, we need to eliminate the square root term by choosing a value for b that makes 40b a perfect square. The least positive integer b > 40 that makes 40b a perfect square is 49. Therefore, H(40,49) is a positive integer.
Step-by-step explanation:
To find the least positive integer b > 40 such that H(40,b) is also a positive integer, we can substitute the values into the given formula:
H(a,b) = (a + √ab + b)/3
By substituting a = 40, we get:
H(40,b) = (40 + √(40b) + b)/3
To find a positive integer b that makes H(40,b) a positive integer, we need to eliminate the square root term. This means that 40b must be a perfect square.
The least positive integer b > 40 that makes 40b a perfect square is 49.
Therefore, H(40,49) is a positive integer.