What is the square root of 5476?

Options

A. 84
B. 76
C. 74
D. 66

Answer

To find the square root of 5476 using the long division method, follow these steps:

### Step-by-Step Solution:

1. **Group the Digits**: Start by grouping the digits of the number 5476 in pairs from right to left. This gives us the pairs (54)(76).

2. **Find the Largest Square**: Look at the first group (54). The largest perfect square less than or equal to 54 is 49 (which is 7^2). So, we write 7 as the first digit of our square root.

3. **Subtract and Bring Down**: Subtract 49 from 54, which gives us 5. Then, bring down the next pair (76) next to 5, making it 576.

4. **Double the Root**: Now, double the number we found (7). This gives us 14. We will use this as 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 (140 + x) * x is less than or equal to 576. Testing with 4:
- (140 + 4) * 4 = 144 * 4 = 576.
This works perfectly.

6. **Subtract Again**: Subtract 576 from 576, which gives us 0. Since there are no more digits to bring down, we have completed the process.

7. **Final Result**: The square root of 5476 is 74.

### Conclusion:
The square root of 5476 is 74.

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