Đáp án+Giải thích các bước giải:
`2\sqrt{27/4}-\sqrt{48/9}-2/5\sqrt{75/16}`
`=\sqrt{27/4*4}-\sqrt{48}/3-2/5*\sqrt{5^2/4^2*3}`
`=\sqrt{27}-\sqrt{16.3}/3-2/5*5/2*\sqrt{3}`
`=3\sqrt3-(4\sqrt3)/3-\sqrt3`
`=2\sqrt3-(4\sqrt3)/3`
`=(6\sqrt3-4\sqrt3)/3`
`=(2\sqrt3)/3`
`\sqrt{7-5}/2-(6-2\sqrt{7})/4+6/(\sqrt{7}-2)-5/(4-\sqrt{7})`
`=\sqrt2/2-(2(3-\sqrt7))/4+(6(\sqrt7+2))/(7-4)-(5(4+\sqrt7))/(16-7)`
`=\sqrt2/2-(3-\sqrt7)/2+(6(\sqrt7+2))/3-(5(4+\sqrt{7}))/9`
`=\sqrt2/2-(3-\sqrt7)/2+2(\sqrt7+2)-(20+5\sqrt7)/9`
`=(9\sqrt2-3.9+9\sqrt7+36\sqrt7+72-40-10\sqrt7)/18`
`=(35\sqrt7+9\sqrt2+5)/18`
`1/(1+sqrt2)+1/(sqrt2+sqrt3)+1/(sqrt3+sqrt4)+....+1/(sqrt{99}+sqrt{100})`
`=(sqrt2-1)/(2-1)+(sqrt3-sqrt2)/(3-2)+(sqrt4-sqrt3)/(4-3)+......+(sqrt{100}-sqrt{99})/(100-99)`
`=sqrt2-1+sqrt3-sqrt2+sqrt4-sqrt3+.....+sqrt{100}-sqrt{99}`
`=sqrt{100}-1`
`=10-1=9`
