Math Problem Statement

32\sqrt{32}

Solution

The square root of 32 can be simplified by factoring it into its prime factors:

32=16×2=16×2=42\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}

So, the simplified form of 32\sqrt{32} is 424\sqrt{2}.

Would you like further clarification or more examples?


  1. What is the square root of 64?
  2. How do you simplify square roots with prime factors?
  3. Can you simplify 50\sqrt{50} the same way?
  4. What are other examples of square roots involving primes?
  5. How do you simplify cube roots?

Tip: To simplify square roots, always try to express the number under the root as a product of squares, as this allows you to simplify the square root effectively!

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Math Problem Analysis

Mathematical Concepts

Square Roots
Simplification of Square Roots
Prime Factorization

Formulas

\sqrt{ab} = \sqrt{a} \times \sqrt{b}

Theorems

Simplifying square roots by prime factorization

Suitable Grade Level

Grades 6-8