The units digit of a perfect square is 6. What are the possible values of the tens digit?
I know the answers are 1, 3, 5, 7, and 9 because
6 * 6 = 36
4 * 4 = 16
ect.
But I want to use modula but I don't know how... :(
+359 To find the possible values of the tens digit of a perfect square with a units digit of 6, we need to consider the squares of integers ending in 4 or 6, as these are the only possibilities for a number to have a units digit of 6 when squared.
Let's denote the perfect square as \( n^2 \), where \( n \) is an integer.
1. If the units digit of \( n \) is 4, then the units digit of \( n^2 \) will be 6.
- For example, if \( n = 24 \), then \( n^2 = 576 \).
2. If the units digit of \( n \) is 6, then the units digit of \( n^2 \) will also be 6.
- For example, if \( n = 26 \), then \( n^2 = 676 \).
From these examples, we can observe that the tens digit of \( n^2 \) can be either 2 or 6.
Therefore, the possible values of the tens digit of a perfect square with a units digit of 6 are \( \boxed{2, 6} \).
