`a)`
`( 2 \sqrt{6} -4 \sqrt{3} + 5 \sqrt{2} - 1/4 \sqrt{8}) . 3 \sqrt{6}`
` = 2 \sqrt{6} . 3 \sqrt{6} - 4 \sqrt{3} . 3 \sqrt{6} + 5 \sqrt{2} . 3 \sqrt{6} - 1/4 \sqrt{8} . 3 \sqrt{6}`
` = 36 - 36 \sqrt{2} + 30 \sqrt{3} - 3 \sqrt{3}`
` = 36 - 36\sqrt{2} + 27 \sqrt{3}`
`b)`
`2 \sqrt{2} (2 -3 \sqrt{3}) + (1 - 2\sqrt{2})^2 + 6 \sqrt{6}`
`= 2 \sqrt{2} . 2 - 2 \sqrt{2} . 3 \sqrt{3} - [ 1^2 - 2 . 1 . 2 \sqrt{2} + (2\sqrt{2})^2] + 6 \sqrt{6}`
`= 4 \sqrt{2} - 6 \sqrt{6} + (1 - 4 \sqrt{2} + 8) + 6 \sqrt{6}`
` = 4 \sqrt{2} - 6 \sqrt{6} + 1 - 4 \sqrt{2} + 8 + 6 \sqrt{6}`
`= 9`
`c)`
`1/(\sqrt{3}-\sqrt{2}) + 1/(\sqrt{3} + \sqrt{2})`
` = ( (\sqrt{3} + \sqrt{2}) + (\sqrt{3} - \sqrt{2}))/((\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}))`
`= (\sqrt{3} + \sqrt{2} + \sqrt{3} - \sqrt{2})/(3-2)`
`= 2 \sqrt{3}`
`d)`
`(3 + 2 \sqrt{3})/(\sqrt{3}) + (2 \sqrt{2})/(\sqrt{2}+1) - (2 + \sqrt{3})`
`= \sqrt{3} + 2 + 4 - 2 \sqrt{2} - 2 - \sqrt{3}`
`= 4 - 2 \sqrt{2}`
