The square root of 16641 is 129.

To find the square root of 16641, we can use the prime factorization method.

Prime Factorization:
1. Start by dividing the number by the smallest prime number, which is 2.
2. If the number is divisible by 2, divide it until it is no longer divisible by 2.
3. Repeat the process with the next prime number, which is 3.
4. Continue dividing by prime numbers until the number becomes 1.

Prime Factorization of 16641:
16641 ÷ 3 = 5547
5547 ÷ 3 = 1849
1849 ÷ 13 = 143
143 ÷ 11 = 13
13 ÷ 13 = 1

Therefore, the prime factorization of 16641 is 3 × 3 × 11 × 13 × 13.

Simplifying the Square Root:
The square root of 16641 can be simplified by grouping the prime factors into pairs.

√(3 × 3 × 11 × 13 × 13)
= √(3 × 3) × √(11 × 13 × 13)
= 3 × √(11 × 13 × 13)

Calculating the Square Root:
Now, we can calculate the square root by taking the square root of each pair of factors and multiplying them together.

√(3 × 3) × √(11 × 13 × 13)
= 3 × √(11) × √(13 × 13)
= 3 × √(11) × 13
= 3 × 13 × √(11)
= 39√(11)

Therefore, the square root of 16641 is 39√(11).

Approximating the Square Root:
To approximate the value of the square root, we can find the perfect square closest to 16641.

The closest perfect squares are:
- For 129, the square is 129² = 16641.
- For 121, the square is 121² = 14641.
- For 211, the square is 211² = 44521.
- For 229, the square is 229² = 52441.

Since 16641 is closer to 129² than any other perfect square, the square root of 16641 is approximately 129.

Therefore, the correct answer is option 'A' - 129.