`(3 sqrt{50} - 5 sqrt{18} + 3 sqrt{8}) . sqrt{2} `
`= 3 sqrt{100} - 5 sqrt{36} + 3 sqrt{16}`
`= 3 . 10 - 5 . 6 + 3 . 4`
`= 30 - 30 + 12`
`= 12`
`sqrt{20} - sqrt{45} + 2 sqrt{5}`
`= 2sqrt{5} - 3sqrt{5} + 2 sqrt{5}`
`= (2-3+2) sqrt{5}`
`= -sqrt{5}`
`2 sqrt{32} - 5 sqrt{27} - 4 sqrt{8} + 3 sqrt{75} `
`= 2 . 4sqrt{2} - 5 . 3sqrt{3} - 4 . 2sqrt{2} + 3 . 5sqrt{3} `
`= 8sqrt{2} - 15sqrt{3} - 8sqrt{2} + 15sqrt{3} `
`= (8sqrt{2} - 8sqrt{2}) + (15sqrt{3} - 15sqrt{3} )`
`= 0+0`
`= 0`
\(\left(3\sqrt{50}-5\sqrt{18}+3\sqrt{8}\right)\cdot\sqrt{2}\)
\(=\left(3\cdot5\sqrt{2}-5\cdot3\sqrt{2}+3\cdot2\sqrt{2}\right)\cdot\sqrt{2}\)
\(=\left(15\sqrt{2}-15\sqrt{2}+6\sqrt{2}\right)\cdot\sqrt{2}=6\sqrt{2}\cdot\sqrt{2}=12\)
\(\sqrt{20}-\sqrt{45}+2\sqrt{5}\)
\(=2\sqrt{5}-3\sqrt{5}+2\sqrt{5}=\sqrt{5}\)
\(2\sqrt{32}-5\sqrt{27}-4\sqrt{8}+3\sqrt{75}\)
\(=2\cdot4\sqrt{2}-5\cdot3\sqrt{3}-4\cdot2\sqrt{2}+3\cdot5\sqrt{3}\)
\(=8\sqrt{2}-15\sqrt{3}-8\sqrt{2}+15\sqrt{3}=0\)
