`a, 2\sqrt{28} + 2\sqrt{32} - \sqrt{112} - 1/3\sqrt{162}`
`= 4\sqrt{7} + 8\sqrt{2} - 4\sqrt{7} - 3\sqrt{2}`
`= 4\sqrt{7} + 5\sqrt{2} - 4\sqrt{7}`
`= 5\sqrt{2}`
`b, \sqrt{31+6\sqrt{12}}.(\sqrt{27}-2)`
`= (3\sqrt{3}+2)(\sqrt{27}-2)`
`= (3\sqrt{3}+2)(3\sqrt{3}-2)`
`= (3\sqrt{3})^2 - 2^2`
`= 23`
`c, (\sqrt{125}-5\sqrt{2})/(\sqrt{5}-\sqrt{2}) - 5/(2+\sqrt{3}) - 15\sqrt{1/3}`
`= 5 - 5/(2+\sqrt{3}) - 5\sqrt{3}`
`= 5 - 5(2 - \sqrt{3}) - 5\sqrt{3}`
`= 5 - 10 + 5\sqrt{3} - 5\sqrt{3}`
`= -5`
