Which of the following cannot be the unit digit of a perfect square number ?

Options

A. 6
B. 1
C. 9
D. 8

Answer

To determine which of the following cannot be the unit digit of a perfect square number, we will analyze the unit digits of the squares of the numbers from 0 to 9.

### Step-by-Step Solution:

1. **List the Numbers and Their Squares:**
- Calculate the squares of numbers from 0 to 9 and note the unit digits.
- \(0^2 = 0\) (unit digit is 0)
- \(1^2 = 1\) (unit digit is 1)
- \(2^2 = 4\) (unit digit is 4)
- \(3^2 = 9\) (unit digit is 9)
- \(4^2 = 16\) (unit digit is 6)
- \(5^2 = 25\) (unit digit is 5)
- \(6^2 = 36\) (unit digit is 6)
- \(7^2 = 49\) (unit digit is 9)
- \(8^2 = 64\) (unit digit is 4)
- \(9^2 = 81\) (unit digit is 1)

2. **Identify the Unique Unit Digits:**
- From the calculations, the unit digits of the perfect squares are:
- 0, 1, 4, 5, 6, 9.
- We can summarize the unit digits obtained from the squares:
- **Possible unit digits of perfect squares:** 0, 1, 4, 5, 6, 9.

3. **Compare with Given Options:**
- The options provided are:
- Option 1: 6
- Option 2: 1
- Option 3: 9
- Option 4: 8
- Now, we check which of these options is not in our list of possible unit digits.

4. **Conclusion:**
- The unit digits 6, 1, and 9 are present in our list of possible unit digits.
- The unit digit 8 is **not** present in our list of possible unit digits.
- Therefore, the answer to the question is **Option 4: 8**.

### Final Answer:
**Option 4: 8 cannot be the unit digit of a perfect square number.**

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