Đáp án+Giải thích các bước giải:
`41)sqrt{29-12sqrt5}`
`=sqrt{20-2.2sqrt5.3+9}`
`=sqrt{(2sqrt5-3)^2}`
`=2sqrt5-3`
`42)sqrt{36+12sqrt5}`
`=sqrt{30+2.sqrt{30}.sqrt6+6}`
`=sqrt{(sqrt30+sqrt6)^2}`
`=sqrt30+sqrt6`
`43)sqrt{35-12sqrt6}`
`=sqrt{27-2.3sqrt3.2sqrt2+8}`
`=sqrt{(3sqrt3-2sqrt2)^2}`
`=3sqrt3-2sqrt2`
`44)sqrt{33+20sqrt2}`
`=sqrt{25+2.5.2sqrt2+8}`
$=\sqrt{(5+2\sqrt2)^2}$
`=5+2sqrt2`
`45)sqrt{36-12sqrt5}`
`=sqrt{30-2.sqrt{30}.sqrt6+6}`
`=sqrt{(sqrt30-sqrt6)^2}`
`=sqrt30-sqrt6`
`46)sqrt{46-6sqrt5}`
`=sqrt{45-2.3sqrt5+1}`
`=sqrt{(3sqrt5-1)^2}`
`=3sqrt5-1`
`47)sqrt{29+12sqrt5}`
`=sqrt{20+2.2sqrt5.3+9}`
`=sqrt{(2sqrt5+3)^2}`
`=2sqrt5+3`
`48)sqrt{27+12sqrt2}`
`=sqrt{3(9+4sqrt2)}`
`=sqrt{3(8+2.2sqrt2+1)}`
`=sqrt{3(2sqrt2+1)^2}`
`=sqrt3(2sqrt2+1)`
`=2sqrt6+sqrt3`
`49)sqrt{49-20sqrt6}`
`=sqrt{25-2.5.2sqrt6+24}`
`=sqrt{(5-2sqrt6)^2}`
`=5-2sqrt6`
`50)sqrt{98-16sqrt3}`
`=sqrt{2(49-8sqrt3)}`
`=sqrt{2(48-2.4sqrt3+1)}`
`=sqrt{2(4sqrt3-1)^2}`
`=sqrt2(4sqrt3-1)`
`=4sqrt6-sqrt2`
`51)sqrt{2-sqrt3}`
`=sqrt{(4-2sqrt3)/2}`
`=sqrt{(3-2sqrt3+1)/2}`
`=sqrt{(sqrt3-1)^2/2}`
`=(sqrt3-1)/sqrt2`
`=(sqrt6-sqrt2)/2`
`52)sqrt{4+sqrt15}`
`=sqrt{(8+2sqrt15)/2}`
`=sqrt{(5+2sqrt{5.3}+3)/2}`
`=sqrt{(sqrt5+sqrt3)^2/2}`
`=(sqrt5+sqrt3)/sqrt2`
`=(sqrt10+sqrt6)/2`
