a)
\(=\sqrt{3^2-2.3.\sqrt{7}+\sqrt{7}^2}\\ =\sqrt{\left(3-\sqrt{7}\right)^2}\\ =\left|3-\sqrt{7}\right|\\ =3-\sqrt{7}\)
b)
\(=\sqrt{\sqrt{17}^2-2.\sqrt{17}.2+2^2}\\ =\sqrt{\left(\sqrt{17}-2\right)^2}\\ =\left|\sqrt{17}-2\right|\\ =\sqrt{17}-2\)
c)
\(=\sqrt{\sqrt{5}^2-2.\sqrt{5}.2+2^2}\\ =\sqrt{\left(\sqrt{5}-2\right)^2}\\ =\left|\sqrt{5}-2\right|\\ =\sqrt{5}-2\)
d)
\(=\sqrt{\sqrt{9}^2-2.\sqrt{9}.\sqrt{6}+\sqrt{6}^2}\\ =\sqrt{\left(\sqrt{9}-\sqrt{6}\right)^2}\\ =\left|\sqrt{9}-\sqrt{6}\right|\\ =\sqrt{9}-\sqrt{6}\)
e: \(=\sqrt{13+2\cdot\sqrt{40}}\)
\(=\sqrt{13+2\cdot\sqrt{8}\cdot\sqrt{5}}\)
\(=\sqrt{\left(2\sqrt{2}+\sqrt{5}\right)^2}=2\sqrt{2}+\sqrt{5}\)
f: \(=\sqrt{45+2\cdot3\sqrt{5}\cdot1+1}\)
\(=\sqrt{\left(3\sqrt{5}+1\right)^2}=3\sqrt{5}+1\)
g: \(=\sqrt{25-2\cdot5\cdot2\sqrt{6}+24}\)
\(=\sqrt{\left(5-2\sqrt{6}\right)^2}=5-2\sqrt{6}\)
h: \(=\sqrt{20-2\cdot2\sqrt{5}\cdot3+9}\)
\(=\sqrt{\left(2\sqrt{5}-3\right)^2}=2\sqrt{5}-3\)
