SOLUTION: for each integer n, its square can be written as n^2 = 10*k+r where r is an integer in the range 0 less than or equal to r less than or equal to 9. Determine which values of r can

Algebra ->  Divisibility and Prime Numbers  -> Lessons -> SOLUTION: for each integer n, its square can be written as n^2 = 10*k+r where r is an integer in the range 0 less than or equal to r less than or equal to 9. Determine which values of r can      Log On


   

Question 803431: for each integer n, its square can be written as n^2 = 10*k+r where r is an integer in the range 0 less than or equal to r less than or equal to 9.
Determine which values of r can occur and which cannot.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
n^2 = 10*k+r  0 < r < 9

r is the units (last) digit of a perfect square
Since 

0²=0
1²=1, 
2²=4, 
3²=9
4²=16
5²=25
6²=36
7²=81
8²=64
9²=81

the last (units) digit of ALL perfect squares can
only be 0,1,4,5,6, or 9.  Thus r can be
0,1,4,5,6, or 9, r cannot be 2,3,7, or 8.
 
02 = 10(0) + 0
12 = 10(0) + 1
22 = 10(0) + 4
32 = 10(0) + 9
42 = 10(1) + 6
52 = 10(2) + 5
62 = 10(3) + 6
72 = 10(4) + 9

Edwin