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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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: \(=2\sqrt{2}+1-3=2\sqrt{2}-2\)

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

c: \(=2-\sqrt{3}+\sqrt{3}-1=1\)