https://file.aiquickdraw.com/mathbot/file/1726321268351hbgfger6.jpg

Let's break down the problem:

Given:
- A number \( n \) when divided by 5 gives a remainder of 3. This means we can express \( n \) as:
  \[
  n = 5k + 3
  \]
  for some integer \( k \).

We need to find the remainder when the square of this number (\( n^2 \)) is divided by 5.

### Step-by-step Solution:
1. Since \( n = 5k + 3 \), let's square \( n \):
   \[
   n^2 = (5k + 3)^2 = 25k^2 + 30k + 9
   \]

2. Simplify \( n^2 \) modulo 5:
   - Notice that each term can be reduced modulo 5:
     - \( 25k^2 \equiv 0 \) (since 25 is a multiple of 5)
     - \( 30k \equiv 0 \) (since 30 is also a multiple of 5)
     - \( 9 \equiv 4 \) (since 9 modulo 5 gives a remainder of 4)

   Therefore,
   \[
   n^2 \equiv 4 \mod 5
   \]

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

Thus, the correct answer is:
\[
\boxed{4} \quad (\text{Option D})
\]

Would you like further explanation or have any other questions? 

Here are some related questions to deepen your understanding:
1. What is the general formula for finding the remainder when squaring a number with a specific remainder?
2. How would the remainder change if the original number had a remainder of 2 when divided by 5?
3. If \( n = 5k + 1 \), what would be the remainder when \( n^2 \) is divided by 5?
4. What patterns can be observed in the squares of numbers modulo 5?
5. How would this problem change if we used a different divisor instead of 5?

**Tip:** When solving problems involving squares and remainders, it's helpful to express the number in a modular form and then simplify the expression step-by-step.

On dividing a number by 5, we get 3 as the remainder. What will the remainder be when the square of this number is divided by 5?

Learn how to solve a modular arithmetic problem involving squaring a number and finding the remainder when divided by 5. This problem involves key concepts in number theory and modular arithmetic, suitable for students in Grades 7-9.

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