The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 17 (B) 16 (C) 15 (C) 14 (E) 13
(A) 17 (B) 16 (C) 15 (C) 14 (E) 13
Make a list of PERFECT SQUARES less than 75:ela07mjt wrote:The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
(A) 17 (B) 16 (C) 15 (C) 14 (E) 13
1² = 1.
2² = 4.
3² = 9.
4² = 16.
5² = 25.
6² = 36.
7² = 49.
8² = 64.
The sum of the 3 values in red is 75:
1²+ 5² + 7² = 1 + 25 + 49 = 75.
Thus, the sum of the 3 integers = 1+5+7 = 13.
The correct answer is E.
