1. The problem is to evaluate the expression $32^{\frac{1}{2}}$. 2. Recall that raising a number to the power of $\frac{1}{2}$ is equivalent to taking the square root of that number. So, $a^{\frac{1}{2}} = \sqrt{a}$. 3. Therefore, $32^{\frac{1}{2}} = \sqrt{32}$. 4. Simplify $\sqrt{32}$ by factoring 32 into its prime factors: $32 = 16 \times 2$. 5. Use the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ to write $\sqrt{32} = \sqrt{16} \times \sqrt{2}$. 6. Since $\sqrt{16} = 4$, we have $\sqrt{32} = 4 \times \sqrt{2}$. 7. Thus, the simplified form of $32^{\frac{1}{2}}$ is $4\sqrt{2}$. 8. In decimal form, $\sqrt{2} \approx 1.414$, so $4 \times 1.414 = 5.656$ approximately. Final answer: $32^{\frac{1}{2}} = 4\sqrt{2} \approx 5.656$