Đáp án+Giải thích các bước giải:
`a)`
`\sqrt{243}-\sqrt{12}-2\sqrt{75}+2\sqrt{27}`
`=\sqrt{81.3}-\sqrt{4.3}-2\sqrt{25.3}+2\sqrt{9.3}`
`=9\sqrt{3}-2\sqrt{3}-10\sqrt{3}+6\sqrt{3}`
`=(9-2-10+6).\sqrt{3}`
`=3\sqrt{3}`
`b)`
`\sqrt{13+4\sqrt{3}}-\sqrt{(3-2\sqrt{3})^2}`
`=\sqrt{12+2.2\sqrt{3}+1}-|3-2\sqrt{3}|`
`=\sqrt{(2\sqrt{3}+1)^2}-(2\sqrt{3}-3)(Vì:2\sqrt{3}>3)`
`=|2\sqrt{3}+1|-2\sqrt{3}+3`
`=2\sqrt{3}+1-2\sqrt{3}+3`
`=4`
`c)`
`(3+2\sqrt{3})/(\sqrt{3})+(2+\sqrt{2})/(\sqrt{2}+1)-(2+\sqrt{3})`
`=(\sqrt{3}.(\sqrt{3}+2))/(\sqrt{3})+(\sqrt{2}.(\sqrt{2}+1))/(\sqrt{2}+1)-(2+\sqrt{3})`
`=\sqrt{3}+2+\sqrt{2}-2-\sqrt{3}`
`=\sqrt{2}`
`d)x≥0;x\ne4`
`((2\sqrt{x}-1)/(x-4)-(1)/(\sqrt{x}+2)):((2\sqrt{x}-1)/(\sqrt{x}-2)-1)`
`=((2\sqrt{x}-1)/((\sqrt{x}+2).(\sqrt{x}-2))-(\sqrt{x}-2)/((\sqrt{x}+2).(\sqrt{x}-2))):((2\sqrt{x}-1-(\sqrt{x}-2))/(\sqrt{x}-2))`
`=(2\sqrt{x}-1-\sqrt{x}+2)/((\sqrt{x}+2).(\sqrt{x}-2)):(2\sqrt{x}-1-\sqrt{x}+2)/(\sqrt{x}-2)`
`=(\sqrt{x}+1)/((\sqrt{x}+2).(\sqrt{x}-2)).(\sqrt{x}-2)/(\sqrt{x}+1)`
`=(1)/(\sqrt{x}+2)`
