Đáp án+Giải thích các bước giải:
\(A= \sqrt{6+ 2\sqrt{2} \sqrt{3-\sqrt{4+2\sqrt{3}}}}\\A= \sqrt{6 +2\sqrt{2}\sqrt{3-\sqrt{(1+\sqrt{3})^2}}}\\A= \sqrt{6+2\sqrt{2}\sqrt{3-(1+\sqrt{3})}}\\A= \sqrt{6+2\sqrt{2[3-(1+\sqrt{3})]}}\\A= \sqrt{6+2\sqrt{2(2-\sqrt{3})}}\\A= \sqrt{6+2\sqrt{4-2\sqrt{3}}}\\A= \sqrt{6+2\sqrt{(1-\sqrt{3})^2}}\\A=\sqrt{6+2(\sqrt{3}-1)}\\A= \sqrt{6+2\sqrt{3}-2}\\A=\sqrt{4+2\sqrt{3}}\\A=\sqrt{(1+\sqrt{3})^2}\\A= 1+\sqrt{3}\\D= \sqrt{2+\sqrt{2}}\sqrt{2+\sqrt{2+\sqrt{2}}}\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{2}}}}\\D= \sqrt{(2+\sqrt{2})(2+\sqrt{2+\sqrt{2}})(2+\sqrt{2+\sqrt{2+\sqrt{2}}})(2-\sqrt{2+\sqrt{2+\sqrt{2}}})}\\D= \sqrt{(2+\sqrt{2})(2+\sqrt{2+\sqrt{2}})[4-(2+\sqrt{2+\sqrt{2}})]}\\D = \sqrt{(2+\sqrt{2})(2+\sqrt{2+\sqrt{2}})(2-\sqrt{2+\sqrt{2}})}\\D = \sqrt{(2+\sqrt{2})[4-(2+\sqrt{2})]}\\D =\sqrt{(2+\sqrt{2})(2-\sqrt{2})}\\D =\sqrt{4-2}\\D=2\\E = \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48 -10\sqrt{7+4\sqrt{3}}}}}\\E =\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{(2+\sqrt{3})^2}}}}\\E= \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48 -10(2+\sqrt{3})}}}\\E = \sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{28-10\sqrt{3}}}}\\E =\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{(5-\sqrt{3})^2}}}\\E =\sqrt{4+\sqrt{5\sqrt{3}+5(5-\sqrt{3})}}\\E= \sqrt{4+\sqrt{5\sqrt{3}+25-5\sqrt{3}}}\\E =\sqrt{4+\sqrt{25}}\\E= \sqrt{4+5}\\E =\sqrt{9}\\E=3\)
