The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these integers?
a) 17
b) 16
c) 15
d) 14
e) 13
a) 17
b) 16
c) 15
d) 14
e) 13
not sure of a better way to do it, but you should know that the largest of the three digits should be less than 9, since 9^2 = 81 is greater than 75. So you have numbers 1 through 8.
From then on, its a plug and chug game. Take 8^2 = 64, leaving 11. There is no combination of 2 numbers whose sum will give you this. Move on.
7^2 = 49, leaving a difference of 26. Are there 2 numbers whose squares sum up to 26? Yes, 5^2 + 1^2 = 25 + 1 = 26.
So your digits are 1,5,7, and sum of these is 13. Choice E.
