Find the square root of :
`7744`

Answer

To find the square root of 7744 using the prime factorization method, we can follow these steps:

### Step-by-Step Solution:

1. **Divide by the smallest prime number (2)**:
- Start with 7744 and divide it by 2.
- \( 7744 \div 2 = 3872 \)

2. **Continue dividing by 2**:
- \( 3872 \div 2 = 1936 \)
- \( 1936 \div 2 = 968 \)
- \( 968 \div 2 = 484 \)
- \( 484 \div 2 = 242 \)
- \( 242 \div 2 = 121 \)

3. **Now divide by the next smallest prime number (11)**:
- \( 121 \div 11 = 11 \)
- \( 11 \div 11 = 1 \)

4. **Write the prime factorization**:
- The prime factorization of 7744 is:
\[ 7744 = 2^6 \times 11^2 \]

5. **Apply the square root**:
- To find the square root, we take the square root of each factor:
\[ \sqrt{7744} = \sqrt{2^6} \times \sqrt{11^2} \]
- This simplifies to:
\[ \sqrt{2^6} = 2^{6/2} = 2^3 = 8 \]
\[ \sqrt{11^2} = 11^{2/2} = 11^1 = 11 \]

6. **Multiply the results**:
- Now, multiply the results of the square roots:
\[ \sqrt{7744} = 8 \times 11 = 88 \]

### Final Answer:
The square root of 7744 is **88**.

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