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

\(=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\)

\(=\sqrt{43+2\cdot\sqrt{450}}\)

\(=\sqrt{25+2\cdot5\cdot3\sqrt{2}+18}\)

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

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

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

= \(\sqrt{43\:+30\sqrt{2}}\) = \(\sqrt{(25+2×5×3\sqrt{2}+18}\) = \(5\:+3\sqrt{2}\)

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)=\(\sqrt{13+30\sqrt{2+\sqrt{\left(\sqrt{8}+1\right)^2}}}\)

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

=\(\sqrt{43+30\sqrt{2}}\)=\(\sqrt{\left(5+3\sqrt{2}\right)^2}\)=\(5+3\sqrt{2}\)

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}=\sqrt{13+30\sqrt{2+\sqrt{\left(1+2\sqrt{2}\right)^2}}}\)

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

\(=\sqrt{13+30\left(1+\sqrt{2}\right)}=\sqrt{43+30\sqrt{2}}=\sqrt{\left(5+3\sqrt{2}\right)^2}\backslash=5+3\sqrt{2}\)

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

\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}+1}}}\)

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

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

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

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

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

Ban vào link này nhé

https://share.icloud.com/photos/0T69uRlJ3wsY5qzsay_zH0wQA

Ta có: \(\sqrt{29+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}+5\sqrt{2}\)

\(=\sqrt{29+30\sqrt{2+\sqrt{8+2\cdot2\sqrt{2}\cdot1+1}}}+5\sqrt{2}\)

\(=\sqrt{29+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}+5\sqrt{2}\)

\(=\sqrt{29+30\sqrt{2+2\sqrt{2}+1}}+5\sqrt{2}\)

\(=\sqrt{29+30\sqrt{2+2\sqrt{2}\cdot1+1}}+5\sqrt{2}\)

\(=\sqrt{29+30\sqrt{\left(\sqrt{2}+1\right)^2}}+5\sqrt{2}\)

\(=\sqrt{29+30\left(\sqrt{2}+1\right)}+5\sqrt{2}\)

\(=\sqrt{29+30\sqrt{2}+30}+5\sqrt{2}\)

\(=\sqrt{9+2\cdot3\cdot5\sqrt{2}+50}+5\sqrt{2}\)

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

\(=3+5\sqrt{2}+5\sqrt{2}=3+10\sqrt{2}\)

\(a,=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\) \(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{20-2.3\sqrt{20}+9}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(\sqrt{20}-3\right)^2}}}\)\(=\sqrt{\sqrt{5}-\sqrt{6-\sqrt{20}}}\)

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

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

\(b,=\sqrt{3+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\) \(=\sqrt{3+30\sqrt{2+\sqrt{8+2\sqrt{8}+1}}}\)

\(=\sqrt{3+30\sqrt{2+\sqrt{\left(\sqrt{8}+1\right)^2}}}\)\(=\sqrt{3+30\sqrt{3+\sqrt{8}}}=\sqrt{3+30\sqrt{2+2\sqrt{2}+1}}\)

\(=\sqrt{3+30\sqrt{\left(\sqrt{2}+1\right)^2}}=\sqrt{3+30\sqrt{2}+30}=\sqrt{33+30\sqrt{2}}\)

a) Ta có: \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5}-3\right)}}\)

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

\(=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{5}+1}\)

=1

b) Ta có: \(\sqrt{3+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)

\(=\sqrt{3+30\sqrt{2+2\sqrt{2}+1}}\)

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

\(=\sqrt{33+30\sqrt{2}}\)