To find the square root of 841 using the prime factorization method, follow these steps:
Step 1: Prime Factorization of 841
- Start by dividing 841 by the smallest prime number, which is 2. Since 841 is odd, it is not divisible by 2.
- Next, try dividing by 3. The sum of the digits (8 + 4 + 1 = 13) is not divisible by 3. So, 841 is not divisible by 3.
- Move to the next prime number, which is 5. Since 841 does not end in 0 or 5, it is not divisible by 5.
- Now, try 7. Dividing 841 by 7 gives a non-integer result.
- Next, try 11. Dividing 841 by 11 also gives a non-integer result.
- Continue this until you reach 29. When you divide 841 by 29, you get 29. Thus, we find:
841 = 29 × 29
Step 2: Writing in Exponential Form
- Since 29 is a prime number, we can write the factorization as:
841 = 29²
Step 3: Finding the Square Root
- The square root of a number can be found by taking the square root of its prime factorization. Thus:
√841 = √(29²) = 29
Conclusion
- Hence, the square root of 841 is:
29