Question

\(\sqrt{5-2\sqrt{2+\sqrt{9+4\sqrt{2}}}}\sqrt{\sqrt{3-\sqrt{4-\sqrt{2-\sqrt{6-4\sqrt{10-4\sqrt{6}}}}}}}\)

Answer 1

\(\sqrt{5-2\sqrt{2+\sqrt{9+4\sqrt{2}}}}\sqrt{\sqrt{3-\sqrt{4-\sqrt{2-\sqrt{6-4\sqrt{10-4\sqrt{6}}}}}}}\)

= \(\sqrt{5-2\sqrt{2+2\sqrt{2}+1}}\sqrt{\sqrt{3-\sqrt{4}-\sqrt{2-\sqrt{6-4\left(\sqrt{6}-2\right)}}}}\)

=\(\sqrt{5-2\sqrt{\left(\sqrt{2}+1\right)^2}}\sqrt{\sqrt{3-\sqrt{4}-\sqrt{2-\sqrt{6-4\sqrt{6}+8}}}}\)

= \(\sqrt{5-2\left(\sqrt{2}+1\right)}\sqrt{\sqrt{3-\sqrt{4}-\sqrt{2-\sqrt{14-4\sqrt{6}}}}}\)

= \(\sqrt{\left(\sqrt{2}-1\right)^2}\sqrt{\sqrt{3-\sqrt{4}-\sqrt{2}-\sqrt{14-4\sqrt{6}}}}\)

= \(\sqrt{\left(\sqrt{2}-1\right)^2}\sqrt{\sqrt{3-\sqrt{4}-\sqrt{2}-\sqrt{14-4\sqrt{6}}}}\)

= \(\left(\sqrt{2}-1\right)\sqrt{\sqrt{3-\sqrt{4}-\sqrt{2}-\sqrt{14-4\sqrt{6}}}}\)

Vế sau kì kì, bạn xem lại thử

Answer 2

\(\sqrt{5-2\sqrt{2+\sqrt{9+4\sqrt{2}}}}\sqrt{\sqrt{3-\sqrt{4-\sqrt{2-\sqrt{6-4\sqrt{10-4\sqrt{6}}}}}}}\)

=\(\sqrt{5-2\sqrt{3+2\sqrt{2}}}\sqrt{\sqrt{3-\sqrt{4-\sqrt{2-\sqrt{6-4\sqrt{6}+8}}}}}\)

=\(\sqrt{4-2\sqrt{2}}\)\(\sqrt{\sqrt{3-\sqrt{4-\sqrt{2-\sqrt{12}-\sqrt{2}}}}}\)

Answer 3

sau thì bạn tiếp tục giải nhé