a) $\sqrt[]{\Bigg(\dfrac{1}{\sqrt[]{2}}-\dfrac{1}{2}\Bigg)^2}$

$=\Bigg|\dfrac{1}{\sqrt[]{2}}-\dfrac{1}{2}\Bigg|$

$=\dfrac{1}{\sqrt[]{2}}-\dfrac{1}{2}$

b) $\sqrt[]{(0,1-\sqrt[]{0,1})^2}$

$=\Bigg|0,1-\sqrt[]{0,1}\Bigg|$

$=-0,1+\sqrt[]{0,1}$

c) $\sqrt[]{(10-5\sqrt[]{2})^2}-\sqrt[]{(4\sqrt[]{2}-7)^2}$

$=\Bigg|10-5\sqrt[]{2}\Bigg|-\Bigg|4\sqrt[]{2}-7\Bigg|$

$=10-5\sqrt[]{2}-(7-4\sqrt[]{2})$

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

d) $\sqrt[]{8+2\sqrt[]{7}}+\sqrt[]{8-2\sqrt[]{7}}$

$=\sqrt[]{(\sqrt[]{7}+1)^2}+\sqrt[]{(\sqrt[]{7}-1)^2}$

$=\Bigg|\sqrt[]{7}+1\Bigg|+\Bigg|\sqrt[]{7}-1\Bigg|$

$=\sqrt[]{7}+1+\sqrt[]{7}-1$

$=2\sqrt[]{7}$

e) $\sqrt[]{9+4\sqrt[]{2}}-\sqrt[]{11-6\sqrt[]{2}}$

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

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

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

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

f) $\sqrt[]{28-10\sqrt[]{3}}+\sqrt[]{13+4\sqrt[]{3}}$

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

$=\Bigg|5-\sqrt[]{3}\Bigg|+\Bigg|2\sqrt[]{3}+1\Bigg|$

$=5-\sqrt[]{3}+2\sqrt[]{3}+1$

$=6+\sqrt[]{3}$

g) $\sqrt[]{14+6\sqrt[]{5}}+\sqrt[]{46+6\sqrt[]{5}}$

$=\sqrt[]{(3+\sqrt[]{5})^2}+\sqrt[]{(3\sqrt[]{5}+1)^2}$

$=\Bigg|3+\sqrt[]{5}\Bigg|+\Bigg|3\sqrt[]{5}+1\Bigg|$

$=3+\sqrt[]{5}+3\sqrt[]{5}+1$

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