Operations with Radical Expressions Color by Number - Free Printable

1. $6\sqrt{3} - 4\sqrt{3} - 10\sqrt{3} = -8\sqrt{3}$ (lilac)
2. $\sqrt{60} + 5\sqrt{60} = 6\sqrt{60} = 6 \cdot 2\sqrt{15} = 12\sqrt{15}$ (seafoam green)
3. $6\sqrt{126} + 3\sqrt{126} + 8\sqrt{126} = 17\sqrt{126} = 17 \cdot \sqrt{9 \cdot 14} = 17 \cdot 3\sqrt{14} = 51\sqrt{14}$ (coral)
4. $6\sqrt{54} - 5\sqrt{24} - 2\sqrt{10} = 6 \cdot 3\sqrt{6} - 5 \cdot 2\sqrt{6} - 2\sqrt{10} = 18\sqrt{6} - 10\sqrt{6} - 2\sqrt{10} = 8\sqrt{6} - 2\sqrt{10}$ (Sky blue)
5. $-\sqrt[3]{320} - 4\sqrt[3]{5} + 2\sqrt[3]{135} + 2\sqrt[3]{16} = -\sqrt[3]{64 \cdot 5} - 4\sqrt[3]{5} + 2\sqrt[3]{27 \cdot 5} + 2\sqrt[3]{8 \cdot 2} = -4\sqrt[3]{5} - 4\sqrt[3]{5} + 2 \cdot 3\sqrt[3]{5} + 2 \cdot 2\sqrt[3]{2} = -8\sqrt[3]{5} + 6\sqrt[3]{5} + 4\sqrt[3]{2} = -2\sqrt[3]{5} + 4\sqrt[3]{2}$ (gold)
6. $\sqrt{3} \cdot \sqrt{6} = \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2}$ (seafoam green)
7. $\sqrt{6} \cdot \sqrt{2} = \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3}$ (lilac)
8. $3\sqrt{3}(2 - \sqrt{5}) = 6\sqrt{3} - 3\sqrt{15}$ (coral)
9. $2\sqrt{15}(\sqrt{6} + 2\sqrt{5}) = 2\sqrt{15} \cdot \sqrt{6} + 4\sqrt{15} \cdot \sqrt{5} = 2\sqrt{90} + 4\sqrt{75} = 2 \cdot 3\sqrt{10} + 4 \cdot 5\sqrt{3} = 6\sqrt{10} + 20\sqrt{3}$ (sky blue)
10. $(\sqrt{2a} - 5)(5\sqrt{2a} - 3) = 5(\sqrt{2a})^2 - 3\sqrt{2a} - 25\sqrt{2a} + 15 = 5(2a) - 28\sqrt{2a} + 15 = 10a - 28\sqrt{2a} + 15$ (gold)
11. $(7 + \sqrt{5})(1 + \sqrt{5}) = 7 + 7\sqrt{5} + \sqrt{5} + 5 = 12 + 8\sqrt{5}$ (sky blue)
12. $\frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5}$ (lilac)
13. $\frac{\sqrt{15}}{\sqrt{12}} = \sqrt{\frac{15}{12}} = \sqrt{\frac{5}{4}} = \frac{\sqrt{5}}{2}$ (coral)
14. $\frac{\sqrt{3}}{2\sqrt{5}} = \frac{\sqrt{15}}{10}$ (seafoam green)
15. $\frac{4\sqrt{2}}{3\sqrt{5}} = \frac{4\sqrt{10}}{15}$ (sky blue)
16. $\frac{\sqrt{3}}{-1 - \sqrt{5}} = \frac{\sqrt{3}(-1 + \sqrt{5})}{(-1 - \sqrt{5})(-1 + \sqrt{5})} = \frac{-\sqrt{3} + \sqrt{15}}{1 - 5} = \frac{-\sqrt{3} + \sqrt{15}}{-4} = \frac{\sqrt{3} - \sqrt{15}}{4}$ (gray)