Đáp án:
`a)2sqrt3+sqrt{(2-sqrt3)^2}`
`=2sqrt3+2-sqrt3`
`=2+sqrt3`
`b)(5+sqrt5)/(5-sqrt5)+(5-sqrt5)/(5+sqrt5)`
`=(5+sqrt5)^2/(25-5)+(5-sqrt5)^2/(25-5)`
`=(25+5+10sqrt5+25+5-10sqrt5)/20`
`=60/20=3`
`c)(sqrt{28}-sqrt{12}-sqrt{7})*sqrt7+2sqrt{21}`
`=(sqrt{4.7}-sqrt{4.3}-sqrt{7})*sqrt7+2sqrt{21}`
`=(2sqrt7-2sqrt3-sqrt7)*sqrt7+2sqrt{21}`
`=(sqrt7-2sqrt3)*sqrt7+2sqrt{21}`
`=7-2sqrt{21}+2sqrt{21}`
`=7`
`d)sqrt{17-3sqrt{32}}+sqrt{17+3sqrt{32}}`
`=sqrt{17-2.3.sqrt8}+sqrt{17+2.3.sqrt8}`
`=sqrt{9-2.3.sqrt8+8}+sqrt{9+2.3.sqrt8+8}`
`=sqrt{(3-sqrt8)^2}+sqrt{(3+sqrt8)^2}`
`=3-sqrt8+3+sqrt8`
`=6`
`e)(2+sqrt5+sqrt3)(2+sqrt5-sqrt3)`
`=(2+sqrt5)^2-sqrt3^2`
`=4+5+4.sqrt5-3`
`=9+4sqrt5-3`
`=6+4sqrt5`
`f)(sqrt{1/3}-sqrt{4/3}+sqrt3):sqrt3`
`=(1/\sqrt3-2/\sqrt3+\sqrt3):\sqrt3`
`=(sqrt3-1/\sqrt3):\sqrt3`
`=sqrt3:\sqrt3-1/\sqrt3:\sqrt3`
`=1-1/3=2/3`
