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

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

\[
32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^5
\]

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

\[
\sqrt{32} = \sqrt{2^5}
\]

We know that:

\[
\sqrt{2^5} = \sqrt{2^4 \times 2} = \sqrt{2^4} \times \sqrt{2} = 2^2 \times \sqrt{2} = 4\sqrt{2}
\]

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

\[
\boxed{4\sqrt{2}}
\]

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

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

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

Learn how to simplify the square root of 32 (sqrt 32) into its simplest radical form, 4 sqrt 2. This detailed step-by-step guide includes prime factorization and simplification techniques for square roots. Suitable for Grades 9-12.

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