1. The problem asks to find the value of $$\sqrt{3^2 \times 5^2}$$ and determine which of the given options it equals. 2. Recall the property of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. 3. Apply this property: $$\sqrt{3^2 \times 5^2} = \sqrt{3^2} \times \sqrt{5^2}$$ 4. Since $$\sqrt{x^2} = x$$ for positive $$x$$, we have: $$\sqrt{3^2} = 3$$ and $$\sqrt{5^2} = 5$$ 5. Multiply these results: $$3 \times 5 = 15$$ 6. Therefore, $$\sqrt{3^2 \times 5^2} = 15$$. 7. Among the options (35^2, 15^2, 15, 35, 15^4), the correct answer is 15.