Hướng dẫn trả lời:
Câu 1:
`A = sqrt24 + 2sqrt54 - 2sqrt96`
`= sqrt{2^2cdot6} + 2sqrt{3^2cdot6} - 2sqrt{4^2cdot6}`
`= 2sqrt{6} + 2cdot3sqrt{6} - 2cdot4sqrt{6}`
`= 2sqrt{6} + 6sqrt{6} - 8sqrt{6}`
`= 0`
Câu 2:
`A = 3sqrt48 + sqrt75 - 2sqrt108`
`= 3sqrt{4^2cdot3} + sqrt{5^2cdot3} - 2sqrt{6^2cdot3}`
`= 3cdot4sqrt{3} + 5sqrt{3} - 2cdot6sqrt{3}`
`= 12sqrt{3} + 5sqrt{3} - 12sqrt{3}`
`= (12sqrt{3} - 12sqrt{3}) + 5sqrt{3}`
`= 5sqrt3`
Câu 3:
`A = sqrt18 - 2sqrt50 + 3sqrt8`
`= sqrt{3^2cdot2} - 2sqrt{5^2cdot2} + 3sqrt{2^2cdot2}`
`= 3sqrt{2} - 2cdot5sqrt{2} + 3cdot2sqrt{2}`
`= 3sqrt{2} - 10sqrt{2} + 6sqrt{2}`
`= -sqrt2`
Câu 4:
`A = sqrt18 + 2sqrt8 - 1/5cdot sqrt50`
`= sqrt{3^2cdot2} + 2sqrt{2^2cdot2} - 1/5cdot sqrt{5^2cdot2}`
`= 3sqrt{2} + 2cdot2sqrt{2} - 1/5cdot5sqrt{2}`
`= 3sqrt{2} + 4sqrt{2} - sqrt{2}`
`= 6sqrt2`
Câu 5:
`M = sqrt20 - sqrt45 + sqrt5`
`= sqrt{2^2cdot5} - sqrt{3^2cdot5} + sqrt5`
`= 2sqrt{5} - 3sqrt{5} + sqrt5`
`= 0`
Câu 6:
`A = sqrt5cdot(sqrt5 - 3) + sqrt45`
`= sqrt5cdot sqrt5 + sqrt5cdot(- 3) + sqrt{3^2cdot5}`
`= 5 - 3sqrt5 + 3sqrt{5}`
`= 5 + (- 3sqrt5 + 3sqrt{5})`
`= 5`
