e. $\dfrac{\sqrt{12}}{\sqrt{3}} + \dfrac{\sqrt{153}}{\sqrt{17}} - \dfrac{\sqrt{304}}{\sqrt{19}} + \dfrac{\sqrt{105}}{\sqrt{2\dfrac{1}{7}}}$
$= \sqrt{\dfrac{12}{3}} + \sqrt{\dfrac{153}{17}} - \sqrt{\dfrac{304}{19}} + \sqrt{\dfrac{105}{\dfrac{15}{7}}}$ 

$= \sqrt{4} + \sqrt{9} - \sqrt{16} + \sqrt{49} = 2 + 3 - 4 + 7 = 8$ 

f. $\dfrac{\sqrt{8 + 4\sqrt{3}}}{\sqrt{2}} + \dfrac{\sqrt{15 - 6\sqrt{6}}}{\sqrt{3}}$ 

$= \dfrac{\sqrt{2(4 + 2\sqrt{3})}}{\sqrt{2}} + \dfrac{\sqrt{3(5 - 2\sqrt{6})}}{\sqrt{3}}$ 

$= \sqrt{(\sqrt{3} + 1)^2} + \sqrt{(\sqrt{3} - \sqrt{2})^2}$ 

$= \sqrt{3} + 1 + \sqrt{3} - \sqrt{2} = 2\sqrt{3} - \sqrt{2} + 1$ 

g. $... = \dfrac{\sqrt{7}(\sqrt{2} - 1)}{1 - \sqrt{2}} + \dfrac{\sqrt{5}(\sqrt{3} - 1)}{1 - \sqrt{3}}]. \dfrac{1}{\sqrt{7} + \sqrt{5}}$ 

$= -(\sqrt{7} + \sqrt{5}).\dfrac{1}{\sqrt{7} + \sqrt{5}} = - 1$ 

h. $... = |2 - \sqrt{3}| (2 + \sqrt{3}) - \dfrac{\sqrt{5}(\sqrt{3} - 1)}{1 - \sqrt{3}}$
$= (2 - \sqrt{3})(2 + \sqrt{3}) + \sqrt{5}$ 

$= 4 - 3 + \sqrt{5} = 1 + \sqrt{5}$

e,

$\frac{\sqrt[]{12}}{\sqrt[]{3}}+\frac{\sqrt[]{153}}{\sqrt[]{17}}-\frac{\sqrt[]{304}}{19}+\frac{\sqrt[]{105}}{2\frac{1}{7}}$

$=$ $\frac{2\sqrt[]{3}}{\sqrt[]{3}}+\frac{3\sqrt[]{17}}{\sqrt[]{17}}-\frac{4\sqrt[]{19}}{\sqrt[]{19}}+$$\frac{7\sqrt[]{\frac{15}{7}}}{\sqrt[]{\frac{15}{7}}}$ 

$=$ $2+3-4+7$

$=$ $8$

f,

$=$ $\frac{\sqrt[]{8+4\sqrt[]{3}}}{\sqrt[]{2}}$ $+$ $\frac{\sqrt[]{15-6\sqrt[]{6}}}{\sqrt[]{3}}$ 

$=$ $\frac{\sqrt[]{2(4+2\sqrt[]{3})}}{\sqrt[]{2}}$ $+$ $\frac{\sqrt[]{3(5-2\sqrt[]{6})}}{\sqrt[]{3}}$ 

$=$ $\sqrt[]{(\sqrt[]{3}+1)^{2}}$ $+$ $\sqrt[]{(\sqrt[]{3}-\sqrt[]{2})^{2}}$

$=$ $\sqrt[]{3}+1+\sqrt[]{3}-\sqrt[]{2}$

$=$ $2\sqrt[]{3}-\sqrt[]{2}+1$

g,

$(\frac{\sqrt[]{14}-\sqrt[]{7}}{1-\sqrt[]{2}}$ $+$ $\frac{\sqrt[]{15}-\sqrt[]{5}}{1-\sqrt[]{3}})$.$\frac{1}{\sqrt[]{7}+\sqrt[]{5}}$

$=$ $(\frac{-\sqrt[]{7}(\sqrt[]{2}-1)}{\sqrt[]{2}-1}$ $+$ $\frac{-\sqrt[]{5}(\sqrt[]{3}-1)}{\sqrt[]{3}-1})$.$\frac{1}{\sqrt[]{7}+\sqrt[]{5}}$

$=$ $-(\sqrt[]{7}+\sqrt[]{5}).\frac{1}{\sqrt[]{7}+\sqrt[]{5}}$ 

$=$ $-1$

h,

$\sqrt[]{(2-\sqrt[]{3})^{2}}.(2+\sqrt[]{3})-\frac{\sqrt[]{15}-\sqrt[]{5}}{1-\sqrt[]{3}}$ 

$=$ $|2-\sqrt[]{3}|.(2+\sqrt[]{3})+\frac{\sqrt[]{5}(\sqrt[]{3}-1)}{\sqrt[]{3}-1}$ 

$=$ $(2-\sqrt[]{3}).(2+\sqrt[]{3})+\sqrt[]{5}$

$=$ $4-3+\sqrt[]{5}$

$=$ $\sqrt[]{5}+1$