A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5 ?

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we need to find the remainder when the square of a number, which leaves a remainder of 3 when divided by 5, is divided by 5.

### Step-by-Step Solution:

1. **Understand the given condition**:
We know that when a number \( n \) is divided by 5, it leaves a remainder of 3. This can be expressed mathematically as:
\[ n \equiv 3 \mod 5 \]

2. **Square the number**:
We need to find \( n^2 \). Since \( n \equiv 3 \mod 5 \), we can square both sides:
\[ n^2 \equiv 3^2 \mod 5 \]
Simplifying this gives:
\[ n^2 \equiv 9 \mod 5 \]

3. **Calculate the remainder of \( 9 \) when divided by \( 5 \)**:
To find the remainder of \( 9 \) when divided by \( 5 \), we perform the division:
\[ 9 \div 5 = 1 \quad \text{(quotient)} \]
The remainder can be calculated as:
\[ 9 - (5 \times 1) = 9 - 5 = 4 \]
Therefore:
\[ 9 \equiv 4 \mod 5 \]

4. **Conclusion**:
Thus, the remainder when the square of the number is divided by 5 is:
\[ n^2 \equiv 4 \mod 5 \]

### Final Answer:
The remainder when the square of the number is divided by 5 is **4**.