\( \begin{array}{ll}\text { 10 } \sqrt{25 a^{6} p^{10}} & \text { 2. } \sqrt[3]{8 x^{12} y^{15}} \\ \text { 3. } \sqrt[5]{32 x^{5} y^{10}} & \text { 4. } \sqrt{2 x^{3}} \times \sqrt{8 x^{5}} \\ \)\begin{tabular}{ll}\text { (5. }\( \sqrt{2} \times \sqrt{8} \) & \text { 6. }\( \sqrt[6]{64 a^{5} b^{12} c^{18}} \) \\ \text { (7) }\( \sqrt{9 x^{10}+16 x^{10}} \) & \text { 8. }\( \sqrt{\frac{27 x^{3} y^{5}}{12 x^{3} y^{3}}} \) \\ \text { 9. }\( \sqrt{3 m^{3}} \times \sqrt{27 m} \) & \text { 10. }\( \sqrt{2 m^{3}} \times \sqrt{50 m x^{2}} \) \\ \text { 11. }\( \frac{\sqrt{9 x^{10}}+\sqrt{4 x^{10}}}{5 x^{3}} \) & \text { 12. }\( \sqrt[3]{3 x} \times \sqrt[3]{72 x^{5}} \) \\ \hline\end{tabular}\end{array}

Did you know that square roots were being used as far back as ancient Babylon? They had a surprising knack for calculations and often relied on geometric methods to find roots long before modern algebra came into play! They would manipulate numbers and shapes, laying the groundwork for the mathematics we know today. In real-world applications, understanding roots is crucial for various fields! For example, in engineering, calculating the area or volume of materials often involves square and cube roots. Similarly, in finance, understanding the rates of return may require knowledge of roots to compute compound interest or growth rates. So next time you encounter a root, remember its real-world significance!