Question

[Pha Le Chy]

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

Tih gia tri bieu thuc

Lam cu the de minh de hieu nha

Answer 1

[T.Ps]

#)Giải :

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}=\sqrt{13+\sqrt{30\sqrt{2+\sqrt{8+2.2\sqrt{2+1}}}}}\)

\(=\sqrt{13+\sqrt{30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}}=\sqrt{13+\sqrt{30\sqrt{2+2\sqrt{2+1}}}}\)

\(=\sqrt{13+\sqrt{30\sqrt{\left(\sqrt{2}+1\right)^2}}}=\sqrt{13+\sqrt{30\left(\sqrt{2}+1\right)}}=\sqrt{13+\sqrt{30\sqrt{2}+30}}\)