To solve the square root of \( 676 \) using prime factorization, we follow these steps:

1. **Prime Factorization of 676**:  
   We begin by finding the prime factors of 676.

   - 676 is an even number, so we divide it by 2:
     \[
     676 \div 2 = 338
     \]
   - Now, 338 is still even, so we divide it by 2 again:
     \[
     338 \div 2 = 169
     \]
   - Next, 169 is not divisible by 2, so we try dividing it by 13:
     \[
     169 \div 13 = 13
     \]
   - So, 169 is \( 13^2 \).

2. **Prime Factors**:  
   Therefore, the prime factorization of 676 is:
   \[
   676 = 2^2 \times 13^2
   \]

3. **Taking the Square Root**:  
   To find the square root of 676, we take the square root of each factor:
   \[
   \sqrt{676} = \sqrt{(2^2) \times (13^2)} = 2 \times 13 = 26
   \]

Thus, the square root of 676 is \( 26 \).

Would you like further details or have any questions?

Here are five related questions for practice:
1. What is the prime factorization of 169?
2. How do you find the square root of 144 using prime factorization?
3. What is the prime factorization of 196, and what is its square root?
4. Can you determine the square root of 1024 using prime factorization?
5. What is the prime factorization of 900, and what is its square root?

**Tip**: Always start by checking divisibility by small primes (2, 3, 5) when finding the prime factorization of a number.

Learn how to find the square root of 676 using prime factorization. This step-by-step guide breaks down the process of prime factorizing 676 and using those factors to compute the square root. Ideal for students in Grades 6-8.

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