`a)`

`(5+3\sqrt{5})/(\sqrt{5})-1/(\sqrt{5}-2)`

`=(\sqrt{5}(\sqrt{5}+3))/(\sqrt{5})-(\sqrt{5}+2)/((\sqrt{5}-2)(\sqrt{5}+2))`

`=\sqrt{5}+3-(\sqrt{5}+2)/(5-4)`

`=\sqrt{5}+3-(\sqrt{5}+2)`

`=\sqrt{5}+3-\sqrt{5}-2`

`=1`

`b)`

`\sqrt{(\sqrt{7}-2)^2}-\sqrt{63}+(\sqrt{56})/(\sqrt{2})`

`=|\sqrt{7}-2|-3\sqrt{7}+2\sqrt{7}`

`=\sqrt{7}-2-3\sqrt{7}+2\sqrt{7}`

`=-2`

`c)`

`(\sqrt{(\sqrt{3}+\sqrt{2})^2}+\sqrt{(\sqrt{3}-\sqrt{2})^2})/(2\sqrt{12})`

`=(|\sqrt{3}+\sqrt{2}|+|\sqrt{3}-\sqrt{2}|)/(2\sqrt{12})`

`=(\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2})/(2\sqrt{12})`

`=(2\sqrt{3})/(2\sqrt{12})`

`=1/(\sqrt{4})=1/2`