Đáp án+Giải thích các bước giải:

 a)

(1+\frac{7-\sqrt{7}}{1-\sqrt{7}}).(1+\frac{7+\sqrt{7}}{1+\sqrt{7}})

=[1+\frac{\sqrt{7}.(\sqrt{7}-1)}{-(\sqrt{7}-1)}].[1+\frac{\sqrt{7}.(\sqrt{7}+1)}{\sqrt{7}+1}]

=(1-\sqrt{7}).(1+\sqrt{7})

=1^{2}-(\sqrt{7})^{2}

=1-7

=-6

b)

\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}

=\frac{3\sqrt{2^{2}.2}-2\sqrt{2^{2}.5}+\sqrt{2^{2}.2}}{3\sqrt{3^{2}.2}-2\sqrt{3^{2}.3}+\sqrt{3^{2}.5}}

=\frac{3.2\sqrt{2}-2.2\sqrt{3}+2\sqrt{5}}{3.3\sqrt{2}-2.3\sqrt{3}+3\sqrt{5}}

=\frac{(\sqrt{2}-\sqrt{3}+\sqrt{5}).(2.3-2.2+2)}{(\sqrt{2}-\sqrt{3}+\sqrt{5}).(3.3-2.3+3)}

=\frac{6-4+2}{9-6+3}

=4/6

=2/3

c)

\frac{\sqrt{9-4\sqrt{5}}}{2-\sqrt{5}}

=\frac{\sqrt{5-4\sqrt{5}+4}}{2-\sqrt{5}}

=\frac{\sqrt{(\sqrt{5})^{2}-2.\sqrt{5}.2+2^{2}}}{-(\sqrt{5}-2)}

=\frac{\sqrt{(\sqrt{5}-2)^{2}}}{-(\sqrt{5}-2)}

=\frac{|\sqrt{5}-2|}{-(\sqrt{5}-2)}

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

=-1