SOLUTION: a five-digit perfect square in the form of 5abc6 has a thousands digit a, hundreds digit b, and tens digit c. if a< b< c, what is the sum of a+b+c?

Question 8845: a five-digit perfect square in the form of 5abc6 has a thousands digit a, hundreds digit b, and tens digit c. if a< b< c, what is the sum of a+b+c?
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
First of allyou posted the question in wrong category.
The number 5abc6 > 50006 ,since sqrt(50006)~ 223.6202138
And we know that if the last digit of a perfect square x^2 is 6 then
the last digit of x must be 4 or 6.
Starting from 224, we try as the table below:
x x^2
--------------
224 50176 a=0, b =1, c = 7,a+b+c = 8
226 51076 No, violates to a < b < c
234 54756 No, violates to a < b < c
236 55696 OK,a+b+c = 20
244 59536 No, violates to a < b < c
246 60516 Stop,too big (the first digit > 5)
Hence, the possible values of a+b+c = 8 or 20.
In my opinion, it should belong to MS Excel,and not a real math
question.
Kenny

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