A perfect square can have 8 as its units digit.

Options

A. True
B. False
C. Cannot be determined
D. none of the above

Answer

To determine whether a perfect square can have 8 as its units digit, we will analyze the units digits of the squares of all digits from 0 to 9.

### Step-by-Step Solution:

1. **Understanding Perfect Squares**:
A perfect square is the square of an integer. We denote an integer as \( y \), and its square as \( x = y^2 \). We need to find out if \( x \) can have 8 as its units digit.

**Hint**: Remember that the units digit of a number is the last digit of that number.

2. **List the Digits from 0 to 9**:
We will consider the digits from 0 to 9, as these are the only possible units digits for any integer.

**Hint**: Write down the numbers 0 through 9 to keep track of their squares.

3. **Calculate the Squares of Each Digit**:
- \( 0^2 = 0 \) (units digit is 0)
- \( 1^2 = 1 \) (units digit is 1)
- \( 2^2 = 4 \) (units digit is 4)
- \( 3^2 = 9 \) (units digit is 9)
- \( 4^2 = 16 \) (units digit is 6)
- \( 5^2 = 25 \) (units digit is 5)
- \( 6^2 = 36 \) (units digit is 6)
- \( 7^2 = 49 \) (units digit is 9)
- \( 8^2 = 64 \) (units digit is 4)
- \( 9^2 = 81 \) (units digit is 1)

**Hint**: As you calculate, note the last digit of each result.

4. **Identify the Units Digits of the Perfect Squares**:
From the calculations above, the units digits of the squares are:
- 0, 1, 4, 9, 6, 5

**Hint**: Write down the unique units digits you found.

5. **Check for the Presence of 8**:
Now, we check if 8 is among the units digits obtained from the squares. The units digits we have are: 0, 1, 4, 5, 6, 9.

**Hint**: Look closely at your list of units digits to see if 8 is included.

6. **Conclusion**:
Since 8 is not present in the list of possible units digits for perfect squares, we conclude that a perfect square cannot have 8 as its units digit.

**Final Answer**: The statement "A perfect square can have 8 as its units digit" is **False**.