Answer :
Final answer:
Given a product of 3125 for 5 positive real numbers, the minimum sum of these numbers is 25, as per the inequalities of means in mathematics.
Explanation:
The product of 5 positive real numbers is given as 3125. In such a situation, the minimum sum of these numbers can be obtained when each of these numbers is equal since the arithmetic mean (AM) is at least equal to the geometric mean(GM). Thus, for the minimum sum, since the the product of the numbers is 3125 (that is, 5^5), each number should be equal to 5.
Therefore, the sum is 5*5 = 25. This result is in line with the inequalities of means in mathematics which states that in any given list of non-negative real numbers, the AM is always greater than or equal to the GM, with equality only when every number in the list is the same.
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