Giải thích các bước giải:
3) $\sqrt[]{8+2\sqrt[]{15}}$
$ = \sqrt[]{3+2.\sqrt[]{3}.\sqrt[]{5}+5}$
$ = \sqrt[]{(\sqrt[]{3}+\sqrt[]{5})^2}$
$ = |\sqrt[]{3}+\sqrt[]{5}|$
$ = \sqrt[]{3}+\sqrt[]{5}$
4) $\sqrt[]{11-2\sqrt[]{30}}$
$ = \sqrt[]{5-2\sqrt[]{5}.\sqrt[]{6}+6}$
$ = \sqrt[]{(\sqrt[]{5}-\sqrt[]{6})^2}$
$ = |\sqrt[]{5}-\sqrt[]{6}|$
$ = \sqrt[]{6}-\sqrt[]{5}$
5) $\sqrt[]{7+2\sqrt[]{10}}$
$ = \sqrt[]{2+2.\sqrt[]{2}.\sqrt[]{5}+5}$
$ = \sqrt[]{(\sqrt[]{2}+\sqrt[]{5})^2}$
$ = |\sqrt[]{2}+\sqrt[]{5}|$
$ =\sqrt[]{2}+\sqrt[]{5}$
6) $\sqrt[]{12-2\sqrt[]{35}}$
$ = \sqrt[]{5-2.\sqrt[]{5}.\sqrt[]{7}+7}$
$ = \sqrt[]{(\sqrt[]{5}-\sqrt[]{7})^2}$
$ =|\sqrt[]{5}-\sqrt[]{7}|$
$ = \sqrt[]{7}-\sqrt[]{5}$
7) $\sqrt[]{6+\sqrt[]{35}}$
$ = \dfrac{\sqrt[]{12+2\sqrt[]{35}}}{\sqrt[]{2}}$
$ = \dfrac{5+2.\sqrt[]{5}.\sqrt[]{7}+7}{\sqrt[]{2}}$
$ = \dfrac{\sqrt[]{(\sqrt[]{5}+\sqrt[]{7})^2}}{\sqrt[]{2}}$
$ = \dfrac{|\sqrt[]{5}+\sqrt[]{7}|}{\sqrt[]{2}}$
$ = \dfrac{\sqrt[]{5}+\sqrt[]{7}}{\sqrt[]{2}}$
