Question

\(\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{3-2\sqrt{2}}}}\)

Rút gọn hộ mik vs <:

Answer 1

\(\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{3-2\sqrt{2}}}}=\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{\left(\sqrt{2}-1\right)^2}}}=\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{2}+8}}=\sqrt{4\sqrt{2}+4\sqrt{18-8\sqrt{2}}}=\sqrt{4\sqrt{2}+4\sqrt{\left(4-\sqrt{2}\right)^2}}=\sqrt{4\sqrt{2}+16-4\sqrt{2}}=\sqrt{16}=4\)

Answer 2

\(\sqrt{4\sqrt{2}+4\sqrt{10-8\sqrt{3-2\sqrt{2}}}}\)

\(=\sqrt{4\sqrt{2}+4\sqrt{10-8\left(\sqrt{2}-1\right)}}\)

\(=\sqrt{4\sqrt{2}+4\cdot\sqrt{18-8\sqrt{2}}}\)

\(=\sqrt{4\sqrt{2}+4\left(4-\sqrt{2}\right)}\)

=4