1. Stating the problem: We need to simplify the expression $$y=3\sqrt{\frac{32t}{4t}}$$ and find a simpler form of $y$. 2. Simplify inside the square root: Inside the root, divide numerator and denominator where possible: $$\frac{32t}{4t} = \frac{32}{4} \cdot \frac{t}{t} = 8 \cdot 1 = 8$$ 3. Substitute back: $$y = 3 \sqrt{8}$$ 4. Simplify the square root: Recall $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$ 5. Multiply by 3: $$y = 3 \times 2\sqrt{2} = 6\sqrt{2}$$ 6. Final answer: $$y = 6\sqrt{2}$$ The expression simplifies to $6\sqrt{2}$.