Hướng dẫn trả lời:
a) `(1 + {6 - sqrt6}/{1 - sqrt6}).({6 + sqrt6}/{1 + sqrt6} + 1)`
`= (1 + {sqrt6.(sqrt6 - 1)}/{- (sqrt6 - 1)}).({sqrt6.(sqrt6 + 1)}/{sqrt6 + 1} + 1)`
`= (1 - sqrt6).(sqrt6 + 1)`
`= 1^2 - (sqrt6)^2`
`= 1 - 6`
`= -5`
b) `{sqrt2 + sqrt3 + sqrt6 + sqrt8 + sqrt16}/{sqrt2 + sqrt3 + sqrt4}`
`= {sqrt2 + sqrt3 + sqrt{2.3} + sqrt{2.4} + sqrt{4.4}}/{sqrt2 + sqrt3 + sqrt4}`
`= {sqrt2 + sqrt3 + sqrt2.sqrt3 + sqrt2.sqrt4 + sqrt4.sqrt4}/{sqrt2 + sqrt3 + sqrt4}`
`= {sqrt2 + sqrt3 + sqrt2.sqrt3 + sqrt2.sqrt4 + 2sqrt4}/{sqrt2 + sqrt3 + sqrt4}`
`= {sqrt2 + sqrt3 + sqrt4 + sqrt2.sqrt2 + sqrt2.sqrt3 + sqrt2.sqrt4}/{sqrt2 + sqrt3 + sqrt4}`
`= {(sqrt2 + sqrt3 + sqrt4) + sqrt2.(sqrt2 + sqrt3 + sqrt4)}/{sqrt2 + sqrt3 + sqrt4}`
`= {(1 + sqrt2).(sqrt2 + sqrt3 + sqrt4)}/{sqrt2 + sqrt3 + sqrt4}`
`= 1 + sqrt2`
c) `{sqrt8 - sqrt12}/{sqrt18 - sqrt48} - {sqrt5 + sqrt27}/{sqrt30 + sqrt162}`
`= {sqrt2.4 - sqrt2.6}/{sqrt2.9 - sqrt2.24} - {sqrt5 + sqrt27}/{sqrt6.5 + sqrt6.27}`
`= {sqrt2.(sqrt4 - sqrt6)}/{sqrt2 .(9 - sqrt2 .sqrt24} - {sqrt5 + 3sqrt3}/{sqrt6. sqrt5 + sqrt6. 3sqrt3}`
`= {sqrt2.(2 - sqrt6)}/{sqrt2.(3 - 2sqrt6)} - {sqrt5 + 3sqrt3}/{sqrt6.(sqrt5 + 3sqrt3)}`
`= {2 - sqrt6}/{3 - 2sqrt6} - {1}/{sqrt6}`
`= {(2 - sqrt6).(3 + 2sqrt6)}/{(3 - 2sqrt6).(3 + 2sqrt6)} - {1}/{sqrt6}`
`= {6 + 4sqrt6 - 3sqrt6 - 12}/{3^2 - (2sqrt6)^2} - {1}/{sqrt6}`
`= {sqrt6 - 6}/{9 - 24} - {1}/{sqrt6}`
`= {sqrt6 - 6}/{-15} - {1}/{sqrt6}`
`= {- (sqrt6 - 6)}/{15} - {1}/{sqrt6}`
`= {6 - sqrt6}/{15} - {1}/{sqrt6}`
`= {2.(6 - sqrt6)}/{30} - {5sqrt6}/{30}`
`= {(12 - 2sqrt6) - 5sqrt6}/{30}`
`= {12 - 2sqrt6 - 5sqrt6}/{30}`
`= {12 - 7sqrt6}/{30}`
Đáp án:
a) `= -5`
b) `= 1 + sqrt2`
c) `= {12 - 7sqrt6}/{30}`
