Evaluate:
`sqrt (576)`

Options

A. 34
B. 44
C. 24
D. 54

Answer

To evaluate \( \sqrt{576} \), we can follow these steps:

### Step 1: Prime Factorization of 576
We start by finding the prime factors of 576.

1. Divide 576 by 2 (the smallest prime number):
\[ 576 \div 2 = 288 \]
2. Divide 288 by 2:
\[ 288 \div 2 = 144 \]
3. Divide 144 by 2:
\[ 144 \div 2 = 72 \]
4. Divide 72 by 2:
\[ 72 \div 2 = 36 \]
5. Divide 36 by 2:
\[ 36 \div 2 = 18 \]
6. Divide 18 by 2:
\[ 18 \div 2 = 9 \]
7. Now, 9 is not divisible by 2, so we divide by the next prime number, which is 3:
\[ 9 \div 3 = 3 \]
8. Finally, divide 3 by 3:
\[ 3 \div 3 = 1 \]

So, the prime factorization of 576 is:
\[ 576 = 2^6 \times 3^2 \]

### Step 2: Pairing the Prime Factors
Next, we will pair the prime factors to simplify the square root.

- From \( 2^6 \), we can form 3 pairs of 2 (since \( 6 \div 2 = 3 \)).
- From \( 3^2 \), we can form 1 pair of 3.

Thus, we have:
\[ \sqrt{576} = \sqrt{(2^2) \times (2^2) \times (2^2) \times (3^2)} \]

### Step 3: Taking the Square Root
Now we take the square root of each pair:
\[ \sqrt{(2^2)} = 2, \quad \sqrt{(2^2)} = 2, \quad \sqrt{(2^2)} = 2, \quad \sqrt{(3^2)} = 3 \]

Now we multiply the results:
\[ 2 \times 2 \times 2 \times 3 = 8 \times 3 = 24 \]

### Final Answer
Thus, we have:
\[ \sqrt{576} = 24 \]

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