+826 The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?
+1245
The numbers $24^2 = 576$ and $56^2 = 3136$ are examples of perfect squares that have a units digits of $6.$
If the units digit of a perfect square is $5,$ then what are the possible values of the tens digit?
If a number ends with 5, its square will end with 25.
So the only possible value of the tens digit is 2.
How to square a number that ends with a 5.
Separate the 5 out of the number.
Change that 5 to 25.
Add 1 to the number that is left.
Multiply that by the original number.
Stick the 25 to the end of the product.
Examples:
152 452 752 1252
1 5 4 5 7 5 12 5
1 25 4 25 7 25 12 25
1 x (1+1) 25 4 x (4+1) 25 7 x (7+1) 25 12 x (12+1) 25
1 x 2 25 4 x 5 25 7 x 8 25 12 x 13 25
225 2025 5625 15625
.
