$\sqrt{82+12\sqrt{42}}$ = $\sqrt{54+12\sqrt{42}+28}$ = $\sqrt{(3\sqrt{6})² +2.3\sqrt{6} + (2\sqrt{7})²}$ = $\sqrt{(3\sqrt{6}+2\sqrt{7})²}$ = ${3\sqrt{6}+2\sqrt{7}}$
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$\sqrt{755-288\sqrt{6}}$ - $\sqrt{56-16\sqrt{6}}$=$\sqrt{512-288\sqrt{6}+243}$ - $\sqrt{8-16\sqrt{6}+48}$ = $\sqrt{(16\sqrt{2})² -2.16.9\sqrt{6} + (9\sqrt{3})²}$ - $\sqrt{(2\sqrt{2})² -2. 2.\sqrt{2}. 4.\sqrt{3} + (4\sqrt{3})²}$ = $\sqrt{(16\sqrt{2}+9\sqrt{3})²}$ - $\sqrt{(2\sqrt{2}+4\sqrt{3})²}$ = $16\sqrt{2}$ + $9\sqrt{3}$ - $2\sqrt{2}$ - $4\sqrt{3}$ = $5\sqrt{3}$ + $14\sqrt{2}$
