1. The problem involves simplifying square roots and performing operations with them. 2. Recall the property of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ and that $$\sqrt{n^2} = n$$ for any positive integer $n$. 3. Simplify each square root: - $$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$$ - $$\sqrt{49} = 7$$ since 49 is a perfect square. - $$\sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$$ - $$\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$$ 4. Add the terms with like radicals: - $$5\sqrt{3} + 4\sqrt{3} = (5 + 4)\sqrt{3} = 9\sqrt{3}$$ 5. For the expression $$\sqrt{36} \sqrt{7}$$: - $$\sqrt{36} = 6$$ - So, $$\sqrt{36} \sqrt{7} = 6\sqrt{7}$$ 6. Volume given is 200 cm³, but no further question is stated for volume. Final answers: - $$\sqrt{72} = 6\sqrt{2}$$ - $$\sqrt{49} = 7$$ - $$\sqrt{75} = 5\sqrt{3}$$ - $$\sqrt{27} = 3\sqrt{3}$$ - $$5\sqrt{3} + 4\sqrt{3} = 9\sqrt{3}$$ - $$\sqrt{36} \sqrt{7} = 6\sqrt{7}$$