1. **State the problem:** Simplify each expression involving squares and square roots. 2. **Recall the rule:** For any positive number $a$, $(\sqrt{a})^2 = a$ because squaring and square rooting are inverse operations. 3. **Calculate each expression:** - $(\sqrt{5})^2 = 5$ - $(\sqrt{16})^2 = 16$ - $(\sqrt{8})^2 = 8$ - $(2\sqrt{9})^2 = (2 \times 3)^2 = 6^2 = 36$ - $(2\sqrt{3})^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12$ - $(4\sqrt{2})^2 = 4^2 \times (\sqrt{2})^2 = 16 \times 2 = 32$ - $(5\sqrt{7})^2 = 5^2 \times (\sqrt{7})^2 = 25 \times 7 = 175$ - $(\sqrt{18})^2 = 18$ - $(5\sqrt{4})^2 = 5^2 \times (\sqrt{4})^2 = 25 \times 4 = 100$ - $(6\sqrt{18})^2 = 6^2 \times (\sqrt{18})^2 = 36 \times 18 = 648$ 4. **Summary:** Squaring a product involving a square root means squaring each factor separately and using $(\sqrt{a})^2 = a$. **Final answers:** 1. 5 2. 16 3. 8 4. 36 5. 12 6. 32 7. 175 8. 18 9. 100 10. 648