The remainder is 3, when a number is divided 5. If the square of this number…

Step-by-Step Solution

1. Define the number: If a number divided by 5 leaves a remainder of 3, the number can be expressed as: Number = 5k + 3 (where k is any integer).

2. Square the number: To find the square of this number, we square the entire expression: (5k + 3)^2 = (5k)^2 + 2(5k)(3) + 3^2 = 25k^2 + 30k + 9

3. Divide by 5: Now, we divide this squared expression by 5 to find the remainder: (25k^2 + 30k + 9) / 5 = (25k^2 / 5) + (30k / 5) + (9 / 5)

4. Simplify: The terms (25k^2 / 5) and (30k / 5) are perfectly divisible by 5 (leaving 0 remainder). The remaining term is 9 / 5, which leaves a remainder of 4.