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a, P = 7 + 2 - 51 + 14 2 = 7 + 2 - 7 + 2 = 0
b, Q = 2 3 + 1 - 1 3 - 2 + 6 3 + 3
= 2 3 - 1 2 + 3 + 2 + 6 3 - 3 6
= 4 + 3

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)=\(\sqrt{13+30\sqrt{2+\sqrt{\left(\sqrt{8}+1\right)^2}}}\)
=\(\sqrt{13+30\sqrt{2+\sqrt{8}+1}}\)=\(\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)=\(\sqrt{13+30\sqrt{2}+30}\)
=\(\sqrt{43+30\sqrt{2}}\)=\(\sqrt{\left(5+3\sqrt{2}\right)^2}\)=\(5+3\sqrt{2}\)

\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
\(=\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)
\(=\sqrt{6+2\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}}\)
\(=\sqrt{6+2\sqrt{4-2\sqrt{3}}}=\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}\)
\(=\sqrt{6+4\sqrt{3}}=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)

A = 3 − 1 + 3 + 1 ( 3 + 1 ) ( 3 − 1 ) + 2 ( 2 − 3 ) 2 = 2 3 3 − 1 + 2 − 3 = 3 + 2 − 3 = 2

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}.\)
\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}+1}}}\)
\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\)
\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)
\(=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)
\(=\sqrt{13+30\left(\sqrt{2}+1\right)}\)
\(=\sqrt{13+30\sqrt{2}+30}=\sqrt{43+30\sqrt{2}}\)

(=)G 3= \(5+2\sqrt{13}+5-2\sqrt{13}+3\sqrt[3]{\left(5+2\sqrt{13}\right)\left(5-2\sqrt{13}\right)}.G\)
(=) G3 = 10 + 3\(\sqrt[3]{25-52}.G\)= 10 -9G (=) G3 + 9G -10 =0 (=) (G-1)(G2 + G +10)= 0 => G=1 ( G2 + G +10\(\ne0\) )

\(2\sqrt{3}-\sqrt{13-4\sqrt{3}}=2\sqrt{3}-\sqrt{13-2.2\sqrt{3}}\)
\(=2\sqrt{3}-\sqrt{\left(2\sqrt{3}\right)^2-2.2\sqrt{3}+1}\)
\(=2\sqrt{3}-\sqrt{\left(2\sqrt{3}-1\right)^2}=2\sqrt{3}-2\sqrt{3}+1=1\)
\(\sqrt{13^2}=\left|13\right|=13\)