State, whether the square of the following numbers is even or odd ?
(i) `23`
(ii) `54`
(iii) `76`
(iv) `75`

Answer

To determine whether the square of the given numbers is even or odd, we will follow these steps:

### Step 1: Calculate the square of each number.

1. **For 23:**
\[ 23^2 = 529 \]

2. **For 54:**
\[ 54^2 = 2916 \]

3. **For 76:**
\[ 76^2 = 5776 \]

4. **For 75:**
\[ 75^2 = 5625 \]

### Step 2: Determine if the squares are even or odd.

1. **For 529:**
- The unit digit is 9, which is not divisible by 2.
- Therefore, \( 529 \) is **odd**.

2. **For 2916:**
- The unit digit is 6, which is divisible by 2.
- Therefore, \( 2916 \) is **even**.

3. **For 5776:**
- The unit digit is 6, which is divisible by 2.
- Therefore, \( 5776 \) is **even**.

4. **For 5625:**
- The unit digit is 5, which is not divisible by 2.
- Therefore, \( 5625 \) is **odd**.

### Final Summary:
- The square of **23** is **odd**.
- The square of **54** is **even**.
- The square of **76** is **even**.
- The square of **75** is **odd**.

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