1a) $\sqrt[]{8+2\sqrt[]{15}}$
= $\sqrt[]{3+2.\sqrt[]{3}.\sqrt[]{5}+5}$
= $\sqrt[]{(\sqrt[]{5}+\sqrt[]{3})^2}$
= $\sqrt[]{5}$ +$\sqrt[]{3}$
b) $\sqrt[]{3+\sqrt[]{8}}$
= $\sqrt[]{1+2.\sqrt[]{2}+2}$
= $\sqrt[]{(\sqrt[]{2}+1)²}$
= 1+$\sqrt[]{2}$
c) $\sqrt[]{11+4\sqrt[]{6}}$
= $\sqrt[]{8+2.2\sqrt[]{2}.\sqrt[]{3}+3}$
= $\sqrt[]{(\sqrt[]{8}+\sqrt[]{3})²}$
= $\sqrt[]{3}$+$\sqrt[]{3}$
d) $\sqrt[]{14-6\sqrt[]{5}}$
= $\sqrt[]{9 - 2.3.\sqrt[]{5}+5}$
= $\sqrt[]{(3-\sqrt[]{5})²}$
= 3 - $\sqrt[]{5}$
e) $\sqrt[]{22-8\sqrt[]{6}}$
= $\sqrt[]{16-2.4.\sqrt[]{6}+6}$
= $\sqrt[]{(4-\sqrt[]{6})²}$
= 4-$\sqrt[]{6}$
f) $\sqrt[]{16-6\sqrt[]{7}}$
= $\sqrt[]{9-2.3.\sqrt[]{7}+7}$
= $\sqrt[]{(3-\sqrt[]{7})²}$
= 3-$\sqrt[]{7}$
