Evaluate `sqrt (2.8)` correct up to two places of decimal.

Answer

To evaluate the square root of 2.8 correct up to two decimal places using the division method, follow these steps:

### Step-by-Step Solution:

1. **Convert 2.8 to a Fraction:**
- Rewrite 2.8 as \( \frac{28}{10} \) or \( 2.8 = \frac{28}{10} = \frac{14}{5} \).
- For the purpose of finding the square root, we will focus on the decimal directly.

2. **Set Up the Division Method:**
- Write 2.8 as 2.80 (to facilitate the division method).
- Pair the digits starting from the decimal point: (2)(80).

3. **Find the Largest Square Less Than or Equal to 2:**
- The largest square less than or equal to 2 is \( 1^2 = 1 \).
- Write 1 above the 2, and subtract \( 1 \) from \( 2 \) to get \( 1 \).

4. **Bring Down the Next Pair:**
- Bring down the next pair (80) next to the remainder (1), making it 180.

5. **Double the Quotient:**
- The current quotient is 1. Double it to get 2.

6. **Find the Next Digit:**
- We need to find a digit \( x \) such that \( (20 + x) \times x \) is less than or equal to 180.
- Testing \( x = 6 \):
- \( (20 + 6) \times 6 = 26 \times 6 = 156 \).
- This works, so write 6 above the line next to 1 (making it 1.6).
- Subtract 156 from 180 to get a remainder of 24.

7. **Bring Down the Next Pair of Zeros:**
- Bring down two zeros to make it 2400.

8. **Repeat the Process:**
- Double the current quotient (1.6) to get 3.2.
- Find \( y \) such that \( (320 + y) \times y \) is less than or equal to 2400.
- Testing \( y = 7 \):
- \( (320 + 7) \times 7 = 327 \times 7 = 2289 \).
- This works, so write 7 next to 1.6 (making it 1.67).
- Subtract 2289 from 2400 to get a remainder of 111.

9. **Final Result:**
- The square root of 2.8, correct up to two decimal places, is approximately **1.67**.