Math Problem Statement

Express in simplest radical form. square root of, 32, end square root 32

Solution

To simplify the square root of 32, we'll start by factoring 32 into its prime factors:

32=2×2×2×2×2=2532 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5

Now, we can express the square root of 32 as:

32=25\sqrt{32} = \sqrt{2^5}

We know that:

25=24×2=24×2=22×2=42\sqrt{2^5} = \sqrt{2^4 \times 2} = \sqrt{2^4} \times \sqrt{2} = 2^2 \times \sqrt{2} = 4\sqrt{2}

Thus, the simplest radical form of 32\sqrt{32} is:

42\boxed{4\sqrt{2}}

Would you like more details or have any questions? Here are some related questions you might find interesting:

  1. How do you simplify 50\sqrt{50}?
  2. What is the simplest radical form of 72\sqrt{72}?
  3. How do you simplify 18\sqrt{18}?
  4. What is the simplest radical form of 128\sqrt{128}?
  5. How do you simplify 80\sqrt{80}?

Tip: When simplifying square roots, look for the largest perfect square factor of the number under the radical.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12