Question

\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\) và \(\sqrt{3}+1\)

Answer 1

Ta có: \(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

\(=\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)

\(=\sqrt{6+2\sqrt{5-\sqrt{1^2+2.2\sqrt{3}+\left(2\sqrt{3}\right)^2}}}\)

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

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

\(=\sqrt{6+2\sqrt{3-2\sqrt{3}+1}}\)

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

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

\(=\sqrt{4+2\sqrt{3}}\)

\(=\sqrt{3}+1\)

Lại có: \(\sqrt{3}+1\)

Đến đây CTV olm hiểu rồi chứ :)

Answer 2

Kém vậy cưng :>