Bài 2: Thực hiện các phép tính sau:
a) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
b) \(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
c) \(\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)\)
d) \(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
Bài 3: Thực hiện các phép tính sau:
a) \(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\dfrac{8}{1-\sqrt{5}}\)
b) \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
Bài 2:
a.
$=2\sqrt{5}-5\sqrt{5}-4\sqrt{5}+11\sqrt{5}$
$=\sqrt{5}(2-5-4+11)=4\sqrt{5}$
b.
$=\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}$
$=\sqrt{(3-\sqrt{6})^2}+\sqrt{(3-2\sqrt{6})^2}$
$=|3-\sqrt{6}|+|3-2\sqrt{6}|=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}$
c.
$=\sqrt{4-2\sqrt{3}}(\sqrt{3}+1)$
$=\sqrt{(\sqrt{3}-1)^2}(\sqrt{3}+1)$
$=|\sqrt{3}-1|(\sqrt{3}+1)=(\sqrt{3}-1)(\sqrt{3}+1)=2$
d.
$=\frac{1}{\sqrt{2}}(\sqrt{6-2\sqrt{5}}+\sqrt{6+2\sqrt{5}})$
$=\frac{1}{\sqrt{2}}(\sqrt{(\sqrt{5}-1)^2}+\sqrt{(\sqrt{5}+1)^2})$
$=\frac{1}{\sqrt{2}}(\sqrt{5}-1+\sqrt{5}+1)$
$=\frac{1}{\sqrt{2}}.2\sqrt{5}=\sqrt{10}$
Bài 3:
a.
\(=\frac{\sqrt{2}.\sqrt{10}(\sqrt{5}+\sqrt{2})}{\sqrt{5}+\sqrt{2}}+\frac{8(1+\sqrt{5})}{(1-\sqrt{5})(1+\sqrt{5})}\)
\(=\sqrt{20}+\frac{8(1+\sqrt{5})}{1-5}=\sqrt{20}-2(1+\sqrt{5})=2\sqrt{5}-2(1+\sqrt{5})=-2\)
b.
\(=\frac{4\sqrt{2}-2\sqrt{3}}{3\sqrt{2}-4\sqrt{3}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{6}(\sqrt{5}+\sqrt{27})}\)
\(=\frac{\sqrt{2}(4-\sqrt{6})}{-\sqrt{3}(4-\sqrt{6})}-\frac{1}{\sqrt{6}}=\frac{\sqrt{2}}{-\sqrt{3}}-\frac{1}{\sqrt{6}}=\frac{-\sqrt{6}}{2}\)
