The expression \( 32^{\frac{1}{2}} \) is asking for the square root of 32.

To simplify:

\[
32^{\frac{1}{2}} = \sqrt{32}
\]

The number 32 can be factored as:

\[
32 = 16 \times 2
\]

So:

\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2}
\]

Therefore, \( 32^{\frac{1}{2}} = 4\sqrt{2} \).

Would you like more details or explanations?

Here are five related questions:
1. What is \( 64^{\frac{1}{2}} \)?
2. How do you simplify cube roots like \( 27^{\frac{1}{3}} \)?
3. What is the decimal approximation of \( 4\sqrt{2} \)?
4. How would you calculate \( 32^{\frac{3}{2}} \)?
5. How do fractional exponents work for negative bases?

**Tip**: Fractional exponents can be interpreted as roots, where the denominator of the fraction indicates the root and the numerator indicates the power.

Understand how to simplify the square root of 32 by applying exponent rules. Learn the process of factoring 32 into its prime components and breaking down square roots step by step. Suitable for students in Grades 8-10.

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