a)
[tex]2 \sqrt{27} = 2 \sqrt{3 \times 3 \times 3} = 2 \times 3 \sqrt{3} = \\ = 6 \sqrt{3} [/tex]
[tex]4 \sqrt{12} = 4 \sqrt{3 \times 2 \times 2} = 4 \times 2 \sqrt{3} = \\ = 8 \sqrt{3} [/tex]
[tex]3 \sqrt{75} = 3 \sqrt{5 \times 5 \times 3} = 3 \times 5 \sqrt{3} = \\ = 15 \sqrt{3} [/tex]
[tex]2 \sqrt{27} + 4 \sqrt{12} - 3 \sqrt{75} = \\ = 8 \sqrt{3} + 15 \sqrt{3} - 5 \sqrt{3} = \\ = 18 \sqrt{3} [/tex]
b)
[tex](5 \sqrt{5} + \sqrt{45} ) \sqrt{5} = \\ = (5 \sqrt{5 } + \sqrt{3 \times 3 \times 5} ) \times \sqrt{5} = \\ = (5 \sqrt{5} + 3 \sqrt{5} ) \times \sqrt{5} = \\ = 5 \sqrt{5 \times 5} + 3 \sqrt{5 \times 5} = \\ = 5 \times 5 + 3 \times 5 = \\ = 25 \times 15 = 40[/tex]
c)
[tex]( \sqrt{18} - \sqrt{6} ) \div \sqrt{2} = \\ = \sqrt{18 \div 2} - \sqrt{6 \div 2} = \\ = \sqrt{9} - \sqrt{3} = \\ = \sqrt{3 \times 3} - \sqrt{3} = \\ = 3 - \sqrt{3} [/tex]
