[tex]1.) [/tex] [tex] \: \frac{1}{2} \sqrt{2 } + \frac{1}{3} \sqrt{2} = \frac{5}{6} \sqrt{2} [/tex]
[tex]2.) \: \sqrt[7]{a} - 3 \sqrt[7]{a} + 5 \sqrt[7]{a} = 3 \sqrt[7]{a} [/tex]
[tex]3.) \: 3b \sqrt{7} - b \sqrt{7} + c \sqrt{7} \\ = (2b + c) \sqrt{7} \\ [/tex]
[tex] 4.) [/tex] [tex]\: \: \sqrt{72} - \sqrt{50} - 3 \sqrt{75} \\ = \sqrt{ {6}^{2} \times 2} - \sqrt{ {5}^{2} \times 2} - 3 \sqrt{ {5}^{2} \times 3} \\ = 6 \sqrt{2} - 5 \sqrt{2} - (3)(5) \sqrt{3} \\ = \sqrt{2 } - 15 \sqrt{3} [/tex]
[tex]5.)[/tex] [tex]\: \: 7 \sqrt{27} - 2 \sqrt{12} - 3 \sqrt{75} \\ = 7 \sqrt{ {3}^{2} \times 3} - 2 \sqrt{{2}^{2} \times 3 } - 3 \sqrt{ {5}^{2} \times 3} \\ = (7)(3) \sqrt{3} - (2)(2) \sqrt{3} - (3)(5) \sqrt{3} \\ = 21 \sqrt{3} - 4 \sqrt{3} - 15 \sqrt{3} \\ = 2 \sqrt{3} [/tex]
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