Evaluate:
`sqrt (10404)`

Answer

To evaluate \( \sqrt{10404} \), we can follow these steps:

### Step 1: Factor the number
First, we will try to factor the number \( 10404 \) to find its prime factors.

### Step 2: Divide by small prime numbers
We can start dividing \( 10404 \) by small prime numbers like \( 2, 3, 5, 7, \) etc.

1. **Divide by 2** (since \( 10404 \) is even):
\[ 10404 \div 2 = 5202 \]
2. **Divide by 2 again**:
\[ 5202 \div 2 = 2601 \]
3. **Now divide by 3** (since the sum of the digits \( 2 + 6 + 0 + 1 = 9 \) is divisible by \( 3 \)):
\[ 2601 \div 3 = 867 \]
4. **Divide by 3 again**:
\[ 867 \div 3 = 289 \]
5. **Now factor \( 289 \)**:
\[ 289 = 17 \times 17 \]

### Step 3: Write the prime factorization
Now we can write the complete factorization of \( 10404 \):
\[ 10404 = 2^2 \times 3^2 \times 17^2 \]

### Step 4: Apply the square root
Now we can take the square root of the factorization:
\[ \sqrt{10404} = \sqrt{2^2 \times 3^2 \times 17^2} \]
Using the property of square roots:
\[ \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \]
We can simplify:
\[ \sqrt{10404} = \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{17^2} = 2 \times 3 \times 17 \]

### Step 5: Calculate the final result
Now we can calculate:
\[ 2 \times 3 = 6 \]
\[ 6 \times 17 = 102 \]

Thus, the final answer is:
\[ \sqrt{10404} = 102 \]