Find square root of no. By using prime factorisation. 2401

To find the square root of 2401 using prime factorization, follow these steps:

1. **Prime Factorization of 2401**:
   Begin by finding the prime factors of 2401 by dividing it with the smallest prime numbers.

   - 2401 ÷ 7 = 343
   - 343 ÷ 7 = 49
   - 49 ÷ 7 = 7
   - 7 ÷ 7 = 1

   So, \( 2401 = 7^4 \).

2. **Finding the Square Root**:
   The square root of a number is found by taking half the power of the prime factors.

   Since \( 2401 = 7^4 \), the square root will be:
   \[
   \sqrt{2401} = 7^{4/2} = 7^2 = 49
   \]

Thus, \( \sqrt{2401} = 49 \).

Would you like more details or further explanations?

Here are 5 related questions for practice:
1. What is the square root of 2025 using prime factorization?
2. How do you find the square root of a number if the prime factorization has odd exponents?
3. What is the prime factorization of 9801, and how do you find its square root?
4. Can you explain how prime factorization helps in finding cube roots?
5. How can you use the prime factorization method to find the square root of 4096?

**Tip**: When using prime

Learn how to find the square root of 2401 using prime factorization with a step-by-step explanation. This problem covers prime factorization and square roots, suitable for students in Grades 7-9.

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