The square root of 7569 is:

Options

A. 87
B. 93
C. 83
D. 77

Answer

To find the square root of 7569 using the tabular method, we will follow these steps:

### Step-by-Step Solution:

1. **Set Up the Number**: Write the number 7569 and group the digits into pairs from right to left. This gives us (75)(69).

2. **Find the Largest Square**: Look for the largest square number less than or equal to the first pair (75). The largest square is 64 (which is 8^2).

3. **Subtract and Bring Down**: Subtract 64 from 75:
\[ 75 - 64 = 11 \]
Now, bring down the next pair (69) next to 11, giving us 1169.

4. **Double the Root**: The root we found so far is 8. Double it to get 16. This will be the starting point for our next divisor.

5. **Find the Next Digit**: We need to find a digit (let's call it 'x') such that (160 + x) * x is less than or equal to 1169.

6. **Test Values for 'x'**:
- For x = 7:
\[ (160 + 7) * 7 = 167 * 7 = 1169 \]
This is equal to 1169, so x = 7 works.

7. **Complete the Square Root**: The square root of 7569 is the number we formed from our calculations, which is 87 (since we had 8 from the first step and 7 from the second).

### Final Answer:
The square root of 7569 is **87**.