Đáp án:
`a)=2\sqrt{5}-3`
`b)=-2`
`c)=\sqrt{6}`
`d)=2+\sqrt{5}`
Giải thích các bước giải `:`
` a) (\sqrt{20}-5)/(2-\sqrt{5}) + 12/(1+\sqrt{5})`
`=(\sqrt{5}(\sqrt{4}-\sqrt{5}))/(\sqrt{4}-\sqrt{5}) + (12(\sqrt{5}-1))/((\sqrt{5}-1)(1+\sqrt{5}))`
`=\sqrt{5}+ (4(3\sqrt{5}-3))/((\sqrt{5})^2 -1)`
`=\sqrt{5}+ (4(3\sqrt{5}-3))/(5-1)`
`=\sqrt{5}+ (4(3\sqrt{5}-3))/4`
`=\sqrt{5}+\sqrt{5}-3`
`=2\sqrt{5}-3`
`b) (\sqrt{15}-\sqrt{12})/(\sqrt{5}-2) - 1/(2-\sqrt{3})`
`=(\sqrt{3}(\sqrt{5}-\sqrt{4}))/(\sqrt{5}-\sqrt{4}) - (2+\sqrt{3})/((2-\sqrt{3})(2+\sqrt{3}))`
`=\sqrt{3} - (2+\sqrt{3})/(2^2 -(\sqrt{3})^2)`
`=\sqrt{3}- (2+\sqrt{3})/(4-3)`
`=\sqrt{3}-(2+\sqrt{3})/1`
`=\sqrt{3}-2-\sqrt{3}`
`=-2`
`c) \sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}`
`=\sqrt{3^2 -2.3.\sqrt{6}+(\sqrt{6})^2}+\sqrt{33-2\sqrt{6^2 .6}}`
`=\sqrt{(3-\sqrt{6})^2}+ \sqrt{33 -2\sqrt{216}}`
`=|3-\sqrt{6}|+ \sqrt{(\sqrt{24})^2 -2.\sqrt{24}.\sqrt{9}+(\sqrt{9})^2}`
`=3-\sqrt{6}+\sqrt{(\sqrt{24}-\sqrt{9})^2}`
`=3-\sqrt{6}+|\sqrt{24}-\sqrt{9}|`
`=3-\sqrt{6}+\sqrt{24}-\sqrt{9}`
`=3-\sqrt{6}+\sqrt{2^2 .6}-\sqrt{3^2}`
`=3-\sqrt{6}+2\sqrt{6}-3`
`=\sqrt{6}`
`d) \sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}`
`=\sqrt{46-2\sqrt{3^2 .5}}-\sqrt{29-2\sqrt{6^2 .5}}`
`=\sqrt{46-2\sqrt{45}}-\sqrt{29-2\sqrt{180}}`
`=\sqrt{(\sqrt{45})^2 -2\sqrt{45}+1}-\sqrt{(\sqrt{20})^2 -2\sqrt{20}.\sqrt{9}+(\sqrt{9})^2}`
`=\sqrt{(\sqrt{45}-1)^2}-\sqrt{(\sqrt{20}-\sqrt{9})^2}`
`=|\sqrt{45}-1|-|\sqrt{20}-\sqrt{9}|`
`=\sqrt{45}-1-\sqrt{20}+\sqrt{9}`
`=\sqrt{3^2 .5}-1-\sqrt{2^2 .5}+\sqrt{3^2}`
`=3\sqrt{5}-1-2\sqrt{5}+3`
`=2+\sqrt{5}`
