`b)`
`\sqrt{11- 6\sqrt{2}} + \sqrt{6 + \sqrt{32} }`
`= \sqrt{ 9 - 6 \sqrt{2} + 2} + \sqrt{ 4 + 4 \sqrt{2} + 2 }`
`= \sqrt{ 3^2 - 2 . 3 . \sqrt{2} + (\sqrt{2})^2} + \sqrt{ 2^2 + 2 . 2 . \sqrt{2} + (\sqrt{2})^2}`
`= \sqrt{ (3 - \sqrt{2})^2} + \sqrt{ (2 + \sqrt{2})^2}`
`= |3 -\sqrt{2}| + |2 + \sqrt{2}|`
`= (3 -\sqrt{2}) + (2+\sqrt{2})`
`= 3 -\sqrt{2} + 2 + \sqrt{2}`
` = 5`
`c)`
` (\sqrt{3} - 2)/(\sqrt{3} + 2) + (\sqrt{3}-1)/(\sqrt{3}-2) + 15/(\sqrt{3})`
`= ((\sqrt{3} -2)(\sqrt{3}-2) + (\sqrt{3} -1)(\sqrt{3}+2))/( (\sqrt{3}+2)(\sqrt{3}-2)) + 5 \sqrt{3}`
` = ( 7 - 4 \sqrt{3} + 1 + \sqrt{3})/ ( (\sqrt{3})^2 - 2^2) + 5 \sqrt{3}`
`=( 8 - 3 \sqrt{3})/(3-4) + 5 \sqrt{3}`
`= - (8 - 3 \sqrt{3}) + 5 \sqrt{3}`
`= 3\sqrt{3}- 8 + 5 \sqrt{3}`
` = 8 \sqrt{3}-8`
