Question

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

Tính\(D=\sqrt{6+2\sqrt{5-\sqrt{29-12\sqrt{5}}}}\)

Answer 1

a,C=\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

=\(\sqrt{13+30\sqrt{2+\sqrt{9+2\sqrt{8}}}}\)=\(\sqrt{13+30\sqrt{2+\sqrt{\left(\sqrt{8}+1\right)^2}}}=\sqrt{13+30\sqrt{2+\sqrt{8}+1}}\)

=\(\sqrt{13+30\sqrt{3+2\sqrt{2}}}=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}=\sqrt{13+30\left(\sqrt{2}+1\right)}\)

=\(\sqrt{13+30\sqrt{2}+30}=\sqrt{43+2.5.3\sqrt{2}}\)

=\(\sqrt{43+2.5.\sqrt{18}}=\sqrt{\left(\sqrt{18}+5\right)^2}=\sqrt{18}+5\)

=> C=\(\sqrt{18}+5\)

Answer 2

Link nè bạn: (Tính D)

https://hoc24.vn/hoi-dap/question/401820.html