`\sqrt{50}+3\sqrt{8}-\sqrt{32}`

`=\sqrt{5^2 .2}+3\sqrt{2^2 .2}-\sqrt{4^2 .2}`

`=5\sqrt{2}+3.2\sqrt{2}-4\sqrt{2}`

`=5\sqrt{2}+6\sqrt{2}-4\sqrt{2}`

`=(5+6-4)\sqrt{2}`

`=7\sqrt{2}`

`\sqrt{8-\sqrt{15}}+\sqrt{8+\sqrt{15}}`

`=(\sqrt{8-\sqrt{15}}+\sqrt{8+\sqrt{15}})/(\sqrt{2})`

`=(\sqrt{2(8-\sqrt{15})}+\sqrt{2(8+\sqrt{15})})/(\sqrt{2})`

`=(\sqrt{16-2\sqrt{15}}+\sqrt{16+2\sqrt{15}})/(\sqrt{2})`

`=(\sqrt{15-2\sqrt{15}+1}+\sqrt{15+2\sqrt{15}+1})/(\sqrt{2})`

`=(\sqrt{(\sqrt{15}-1)^2}+\sqrt{(\sqrt{15}+1)^2})/(\sqrt{2})`

`=(|\sqrt{15}-1|+|\sqrt{15}+1|)/(\sqrt{2})`

`=(\sqrt{15}-1+\sqrt{15}+1)/(\sqrt{2})`

`=(2\sqrt{15})/(\sqrt{2})`

`=\sqrt{2}.\sqrt{15}`

`=\sqrt{30}`

`\sqrt{7+2\sqrt{6}}-\sqrt{7-2\sqrt{6}}`

`=\sqrt{6+2\sqrt{6}+1}-\sqrt{6-2\sqrt{6}+1}`

`=\sqrt{(\sqrt{6}+1)^2}-\sqrt{(\sqrt{6}-1)^2}`

`=|\sqrt{6}+1|-|\sqrt{6}-1|`

`=\sqrt{6}+1-\sqrt{6}+1`

`=2`