g) $\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}$
$=\dfrac{\sqrt{2}-\sqrt{2-\sqrt{3}}}{(\sqrt{2}+\sqrt{2+\sqrt{3}})(\sqrt{2}-\sqrt{2-\sqrt{3}})}+\dfrac{\sqrt{2}+\sqrt{2-\sqrt{3}}}{(\sqrt{2}+\sqrt{2+\sqrt{3}})(\sqrt{2}-\sqrt{2-\sqrt{3}})}$
$=\dfrac{\sqrt{2}-\sqrt{2-\sqrt{3}}+\sqrt{2}+\sqrt{2-\sqrt{3}}}{2-\sqrt{2(2-\sqrt{3})}+\sqrt{2(2+\sqrt{3})}-\sqrt{(2+\sqrt{3})(2-\sqrt{3})}}$
$=\dfrac{2\sqrt{2}}{2-\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}-\sqrt{4-3}}$
$=\dfrac{2\sqrt{2}}{2-(\sqrt{3}-1)+(\sqrt{3}+1)-1}$
$=\dfrac{2\sqrt{2}}{3}$
h) $\dfrac{5\sqrt{3}+3\sqrt{5}}{\sqrt{15}}+\dfrac{\sqrt{2}}{\sqrt{4}+\sqrt{15}}$
$=\dfrac{(5\sqrt{3}+3\sqrt{5})(\sqrt{4}-\sqrt{15})+\sqrt{30}}{\sqrt{15}(\sqrt{4+\sqrt{15}})}$
$=\dfrac{10\sqrt{3}-15\sqrt{5}+6\sqrt{5}-15\sqrt{3}+\sqrt{30}}{\sqrt{15(4+\sqrt{15})}}$
$=\dfrac{-5\sqrt{3}-9\sqrt{5}+\sqrt{30}}{\sqrt{60+15\sqrt{15}}}$
$=\dfrac{5\sqrt{3(4+\sqrt{15})}+3\sqrt{5(4+\sqrt{15})}+\sqrt{30}}{\sqrt{15}.\sqrt{4+\sqrt{15}}}$
$=\dfrac{5\sqrt{12+3\sqrt{15}}+3\sqrt{20+5\sqrt{15}}+\sqrt{30}}{\sqrt{15}.\sqrt{4+\sqrt{15}}}$
...
i) $\dfrac{7}{2\sqrt{2}-1}+\dfrac{1}{\sqrt{2}-2}$
$=\dfrac{7}{(\sqrt{2}-1)(2+\sqrt{2}+1)}+\dfrac{1}{\sqrt{2}(1-\sqrt{2})}$
$=\dfrac{7\sqrt{2}-3-\sqrt{2}}{\sqrt{2}(\sqrt{2}-1)(3+\sqrt{2})}$
$=\dfrac{6\sqrt{2}-3}{4-\sqrt{2}}$
$=\dfrac{3(2\sqrt{2}-1)}{\sqrt{2}(2\sqrt{2}-1)}$
$=\dfrac{3\sqrt{2}}{2}$
