Đáp án + Giải thích các bước giải:
Câu 4:
`sqrt((2sqrt2-3)^2)-sqrt(27+10sqrt2)`
`=|2sqrt2-3|-sqrt(25+2.5.sqrt2+2)`
`=3-2sqrt2-sqrt((5+sqrt2)^2)`
`=3-2sqrt2-|5+sqrt2|`
`=3-2sqrt2-5-sqrt2`
`=-2-3sqrt2`
Câu 6:
`\frac{2}{sqrt7-sqrt5}-1/3sqrt63+1/4sqrt20`
`=\frac{2(sqrt7+sqrt5)}{(sqrt7-sqrt5)(sqrt7+sqrt5)}-1/3. 3sqrt7+1/4 . 2sqrt5`
`=\frac{2(sqrt7+sqrt5)}{7-5}-sqrt7+1/2 sqrt5`
`=sqrt7+sqrt5-sqrt7+1/2 sqrt5`
`=3/2 sqrt5`
Câu 8:
`\frac{sqrt(7+3sqrt5)}{sqrt2}-2/(sqrt5-1)`
`=\frac{sqrt2.sqrt(7+3sqrt5)}{2}-(2(sqrt5+1))/((sqrt5-1)(sqrt5+1))`
`=\frac{sqrt(14+6sqrt5)}{2}-(2(sqrt5+1))/(5-1)`
`=\frac{sqrt(9+2.3.sqrt5+5)}{2}-(2(sqrt5+1))/(4)`
`=\frac{sqrt((3+sqrt5)^2)}{2}-(sqrt5+1)/(2)`
`=\frac{|3+sqrt5|}{2}-(sqrt5+1)/(2)`
`=\frac{3+sqrt5-sqrt5-1}{2}`
`=\frac{2}{2}=1`
Câu 9:
`\frac{6+3sqrt3}{sqrt3+2}+1/(1-sqrt3)-(sqrt3)/(1+sqrt3)`
`=\frac{3(2+sqrt3)(sqrt3-2)}{(sqrt3+2)(sqrt3-2)}+(1+sqrt3)/((1-sqrt3)(1+sqrt3))-(sqrt3(1-sqrt3))/((1+sqrt3)(1-sqrt3))`
`=\frac{3(3-4)}{3-4}+(1+sqrt3)/(1-3)-(sqrt3-3)/(1-3)`
`=3-(1+sqrt3)/(2)+(sqrt3-3)/(2)`
`=\frac{3.2-1-sqrt3+sqrt3-3}{2}`
`=\frac{2}{2}=1`
