[tex]\displaystyle 1).a=6 \sqrt{3} + \sqrt{108} -4 \sqrt{75} +2 \sqrt{147} \\ a=6 \sqrt{3} +6 \sqrt{3} -4 \cdot 5 \sqrt{3} +2 \cdot 7 \sqrt{3} \\ a=6 \sqrt{3} +6 \sqrt{3} -20 \sqrt{3} +14 \sqrt{3} \\ a=6 \sqrt{3} \\ b=8 \sqrt{3} +33 \sqrt{12} -5 \sqrt{27} \\ b=8 \sqrt{3} +33 \cdot 2 \sqrt{3} -5 \cdot 3 \sqrt{3} \\ b=8 \sqrt{3} +66 \sqrt{3} -15 \sqrt{3} \\ b=59 \sqrt{3} \\ \\ m_a= \frac{6 \sqrt{3} +59 \sqrt{3} }{2} = \frac{65 \sqrt{3} }{2} [/tex]
[tex]\displaystyle 2).a=3 \sqrt{2} +11 \sqrt{7} -2 \sqrt{112} - \sqrt{200} \\ a=3 \sqrt{2} +11 \sqrt{7} -2 \cdot 4 \sqrt{7} -10 \sqrt{2} \\ a=3 \sqrt{2} +11 \sqrt{7} -8 \sqrt{7} -10 \sqrt{2} \\ a=-7 \sqrt{2} +3 \sqrt{7} \\ b=3 \sqrt{28} +2 \sqrt{63} - \sqrt{252} - \sqrt{175} \\ b= 3 \cdot 2 \sqrt{7} +2 \cdot 3 \sqrt{7} -6 \sqrt{7} -5 \sqrt{7} \\ b=6 \sqrt{7} +6 \sqrt{7} -6 \sqrt{7} -5 \sqrt{7} \\ b= \sqrt{7} \\ \\ m_a= \frac{-7 \sqrt{2} +3 \sqrt{7} + \sqrt{7} }{2} = \frac{-7 \sqrt{2} +4 \sqrt{7} }{2} [/tex]
[tex]\displaystyle 3).a=22 \sqrt{7} - \sqrt{648} - \sqrt{567} +2 \sqrt{162} \\ a=22 \sqrt{7} -18 \sqrt{2} -9 \sqrt{7} +2 \cdot 9 \sqrt{2} \\ a=22 \sqrt{7} -18 \sqrt{2} -9 \sqrt{7} +18 \sqrt{2} \\ a=13 \sqrt{7} \\ b=3 \sqrt{567} - \sqrt{800} +2 \sqrt{200} +10 \sqrt{175} \\ b=3 \cdot 9 \sqrt{7} -20 \sqrt{2} +2 \cdot 10 \sqrt{2} +10 \cdot 5 \sqrt{7} \\ b=27 \sqrt{7} -20 \sqrt{2} +20 \sqrt{2} +50 \sqrt{7} \\ b=77 \sqrt{7} \\ \\ m_a= \frac{13 \sqrt{7}+77 \sqrt{7} }{2} = \frac{90 \sqrt{7} }{2} =45 \sqrt{7} [/tex]
