1. The problem is to simplify the expression $0.16 \sqrt{32}$. 2. Recall that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, so we can simplify $\sqrt{32}$ by factoring 32 into a perfect square and another number. 3. Factor 32 as $16 \times 2$, so $\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4 \sqrt{2}$. 4. Substitute back into the expression: $0.16 \times 4 \sqrt{2}$. 5. Multiply the constants: $0.16 \times 4 = 0.64$. 6. The simplified expression is $0.64 \sqrt{2}$. 7. If you want a decimal approximation, $\sqrt{2} \approx 1.414$, so $0.64 \times 1.414 \approx 0.905$. Final answer: $0.64 \sqrt{2}$ or approximately $0.905$.