Math Problem Statement

Simplify \( \sqrt{461} \)

Solution

The problem visible in the uploaded image is:

3. Simplify 461\sqrt{461}

Solution:

We simplify 461\sqrt{461}:

  • Prime Factorization of 461:

    • 461 is a prime number. It cannot be factored further.
  • Since there are no repeated factors under the square root, 461\sqrt{461} cannot be simplified further.

Final Answer:

461\sqrt{461}

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Related Questions:

  1. How do you determine if a number is prime?
  2. What are the steps to simplify square roots when the number is not prime?
  3. How do you estimate square roots of non-perfect squares?
  4. Can 461\sqrt{461} be approximated as a decimal, and how?
  5. What is the significance of prime factorization in simplifying square roots?

Tip:

For simplifying square roots, always start by checking the prime factorization of the number to identify pairs of factors.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization

Formulas

\( \sqrt{n} \) where \( n \) is a non-perfect square

Theorems

Prime Factorization Theorem

Suitable Grade Level

Grades 8-10