Find the square root of `484`.

Options

A. `32`
B. `22`
C. `26`
D. `28`

Answer

To find the square root of 484 using the long division method, we can follow these steps:

### Step-by-Step Solution:

1. **Pair the Digits**: Start from the right and pair the digits of the number. For 484, we have:
- The first pair is `4` (from the left).
- The second pair is `84`.

2. **Find the Largest Square**: Look for the largest number whose square is less than or equal to the first pair (4).
- The number `2` works because \(2 \times 2 = 4\).
- Write `2` above the pair `4` and subtract \(4\) from \(4\) which gives us \(0\).

3. **Bring Down the Next Pair**: Bring down the next pair (84) next to the remainder (0) to form `084` or simply `84`.

4. **Double the Quotient**: Double the number above (which is `2`), giving us `4`. Write this `4` down.

5. **Find the Next Digit**: Now we need to find a digit `x` such that:
- \( (40 + x) \times x \leq 84 \).
- Testing `2`: \( (40 + 2) \times 2 = 42 \times 2 = 84 \) which works.

6. **Subtract**: Write `2` above the `84` and subtract \(84\) from \(84\) to get \(0\).

7. **Conclusion**: Since there are no more pairs to bring down and the remainder is `0`, the square root of `484` is `22`.

### Final Answer:
The square root of `484` is \(22\).

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