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
D. 14
E. 13
Make a list of the perfect squares less than 75. (A
perfect square is the square of an integer):
1^2 = 1
2^2 = 4
3^3 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
Now look in the list above for three perfect squares that can be added to yield a sum of 75:
1+25+49 = 75.
Thus, the integers needed are 1, 5 and 7.
Sum = 1+5+7 = 13.
The correct answer is E.[/
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