1) $5\sqrt{3} - 3\sqrt{3} + 4\sqrt{8} = 2\sqrt{3} + 4\sqrt{8} = 2\sqrt{3} + 4 \cdot 2\sqrt{2} = 2\sqrt{3} + 8\sqrt{2}$
2) $11\sqrt{28} + \sqrt{7} + 2\sqrt{7} = 11\sqrt{4 \cdot 7} + 3\sqrt{7} = 11 \cdot 2\sqrt{7} + 3\sqrt{7} = 22\sqrt{7} + 3\sqrt{7} = 25\sqrt{7}$
3) $24\sqrt{5} - 9\sqrt{5} = 15\sqrt{5}$
4) $-3\sqrt{11} - 2\sqrt{44} - 5\sqrt{10} = -3\sqrt{11} - 2\sqrt{4 \cdot 11} - 5\sqrt{10} = -3\sqrt{11} - 2 \cdot 2\sqrt{11} - 5\sqrt{10} = -3\sqrt{11} - 4\sqrt{11} - 5\sqrt{10} = -7\sqrt{11} - 5\sqrt{10}$
5) $\sqrt{18} + 8\sqrt{27} - 7\sqrt{3} = \sqrt{9 \cdot 2} + 8\sqrt{9 \cdot 3} - 7\sqrt{3} = 3\sqrt{2} + 8 \cdot 3\sqrt{3} - 7\sqrt{3} = 3\sqrt{2} + 24\sqrt{3} - 7\sqrt{3} = 3\sqrt{2} + 17\sqrt{3}$
6) $-2\sqrt{20} + 2\sqrt{45} - \sqrt{5} = -2\sqrt{4 \cdot 5} + 2\sqrt{9 \cdot 5} - \sqrt{5} = -2 \cdot 2\sqrt{5} + 2 \cdot 3\sqrt{5} - \sqrt{5} = -4\sqrt{5} + 6\sqrt{5} - \sqrt{5} = \sqrt{5}$
7) $-9\sqrt{15} + 10\sqrt{15} = \sqrt{15}$
8) $-3\sqrt{24} - \sqrt{6} = -3\sqrt{4 \cdot 6} - \sqrt{6} = -3 \cdot 2\sqrt{6} - \sqrt{6} = -6\sqrt{6} - \sqrt{6} = -7\sqrt{6}$
Parent Tip: Review the logic above to help your child master the concept of adding subtracting and multiplying radicals worksheet.
