Đáp án:
`a)A=\sqrt{3}`
`b)B=1`
`c)C=2`
`d)D=-1`
Giải thích các bước giải:
`a)A=\sqrt{12}-2\sqrt{48}+7/5\sqrt{75}`
`=\sqrt{2^2 .3}-2\sqrt{4^2 .3}+7/5\sqrt{5^2 .3}`
`=2\sqrt{3}-2.4\sqrt{3}+7/5 .5\sqrt{3}`
`=2\sqrt{3}-8\sqrt{3}+7\sqrt{3}`
`=\sqrt{3}`
`b)B=\sqrt{14-6\sqrt{5}}+\sqrt{(2-\sqrt{5})^2}`
`=\sqrt{9-6\sqrt{5}+5}+|2-\sqrt{5}|`
`=\sqrt{3^2-2.3.\sqrt{5}+(\sqrt{5})^2}+\sqrt{5}-2`
`=\sqrt{(3-\sqrt{5})^2}+\sqrt{5}-2`
`=|3-\sqrt{5}|+\sqrt{5}-2`
`=3-\sqrt{5}+\sqrt{5}-2`
`=(3-2)+(-\sqrt{5}+\sqrt{5})`
`=1`
`c)C=(\sqrt{6}-\sqrt{2})\sqrt{2+\sqrt{3}}`
`=\sqrt{2}(\sqrt{3}-1)\sqrt{2+\sqrt{3}}`
`=(\sqrt{3}-1)\sqrt{(\sqrt{2})^2 (2+\sqrt{3})`
`=(\sqrt{3}-1)\sqrt{2(2+\sqrt{3})`
`=(\sqrt{3}-1)\sqrt{4+2\sqrt{3}`
`=(\sqrt{3}-1)\sqrt{3+2\sqrt{3}+1}`
`=(\sqrt{3}-1)\sqrt{(\sqrt{3})^2+2.\sqrt{3}.1+1^2}`
`=(\sqrt{3}-1)\sqrt{(\sqrt{3}+1)^2}`
`=(\sqrt{3}-1)|\sqrt{3}+1|`
`=(\sqrt{3}-1)(\sqrt{3}+1)`
`=(\sqrt{3})^2-1^2`
`=3-1`
`=2`
`d)D=(5+\sqrt{5})/(\sqrt{5}+2)+(\sqrt{5}-5)/\sqrt{5}-11/(2\sqrt{5}+3)`
`=((5+\sqrt{5})(\sqrt{5}-2))/[(\sqrt{5}+2)(\sqrt{5}-2)]+(\sqrt{5}(1-\sqrt{5}))/\sqrt{5}-[11(2\sqrt{5}-3)]/[(2\sqrt{5}+3)(2\sqrt{5}-3)]`
`=(5\sqrt{5}-10+5-2\sqrt{5})/(5-4)+1-\sqrt{5}-[11(2\sqrt{5}-3)]/(20-9)`
`=3\sqrt{5}-5+1-\sqrt{5}-[11(2\sqrt{5}-3)]/11`
`=3\sqrt{5}-5+1-\sqrt{5}-(2\sqrt{5}-3)`
`=3\sqrt{5}-5+1-\sqrt{5}-2\sqrt{5}+3`
`=(3\sqrt{5}-\sqrt{5}-2\sqrt{5})+(-5+1+3)`
`=-1`
