A number when divided by 5 leaves a remainder 3. What is the remainder when…

Solution: Find the remainder when the square is divided by 5.

1. Let the number be k. Since dividing by 5 leaves remainder 3, write k = 5n + 3 for some integer n.

2. Square both sides: k^2 = (5n + 3)^2 = 25n^2 + 30n + 9.

3. The terms 25n^2 and 30n are multiples of 5, so they leave remainder 0 when divided by 5.

4. Only 9 contributes to the remainder: 9 mod 5 = 4.

5. Therefore, the remainder when the square is divided by 5 is 4.