Hướng dẫn trả lời:
Câu 7:
a) `A = 4sqrt3 - sqrt27`
`= 4sqrt3 - sqrt{3^3}`
`= 4sqrt3 - 3sqrt3`
`= sqrt3`
b) `B = sqrt{(sqrt5 - 1)^2} - sqrt5`
`= |sqrt5 - 1| - sqrt5`
`= (sqrt5 - 1) - sqrt5` (Vì `sqrt5 - 1 > 0`)
`= sqrt5 - 1 - sqrt5`
`= (sqrt5 - sqrt5) - 1`
`= -1`
Câu 8:
a) `A = 3sqrt18 + 2sqrt8 - sqrt72`
`= 3sqrt{3^2cdot2} + 2sqrt{2^2cdot2} - sqrt{6^2cdot2}`
`= 3cdot3sqrt{2} + 2cdot2sqrt{2} - 6sqrt{2}`
`= 9sqrt{2} + 4sqrt{2} - 6sqrt{2}`
`= 7sqrt{2}`
b) `B = {sqrt3 - sqrt6}/{1 - sqrt2} + sqrt{(2 - sqrt3)^2}`
`= {sqrt3cdot(1 - sqrt2)}/{1 - sqrt2} + |2 - sqrt3|`
`= sqrt3 + (2 - sqrt3)` (Vì `2 = sqrt4 > sqrt3 → 2 - sqrt3 > 0`)
`= sqrt3 + 2 - sqrt3`
`= (sqrt3 - sqrt3) + 2`
`= 2`
Câu 9:
a) `A = sqrt75cdot5sqrt{(1 - sqrt3)^2}`
`= sqrt{5^2cdot3}cdot5cdot|1 - sqrt3|`
`= 5sqrt{3}cdot5cdot(sqrt3 - 1)` (Vì `sqrt3 - 1 > 0`)
`= 25sqrt{3}cdot(sqrt3 - 1)`
`= 25sqrt{3}cdot sqrt3 + 25sqrt{3}cdot(- 1)`
`= 25cdot3 - 25sqrt{3}`
`= 75 - 25sqrt{3}`
b) `B = {sqrt10 - sqrt6}/{sqrt5 - sqrt3} - 1/{sqrt2 + 1}`
`= {sqrt2cdot(sqrt5 - sqrt3)}/{sqrt5 - sqrt3} - 1/{sqrt2 + 1}`
`= sqrt2 - 1/{sqrt2 + 1}`
`= {sqrt2cdot(sqrt2 + 1) - 1}/{sqrt2 + 1}`
`= {sqrt2cdot sqrt2 + sqrt2cdot1 - 1}/{sqrt2 + 1}`
`= {2 + sqrt2 - 1}/{sqrt2 + 1}`
`= {sqrt2 + (2 - 1)}/{sqrt2 + 1}`
`= {sqrt2 + 1}/{sqrt2 + 1}`
`= 1`
Câu 10:
`A = {sqrt15 - sqrt3}/{sqrt5 - 1} - 1/{2 - sqrt3}`
`= {sqrt3cdot(sqrt5 - 1)}/{sqrt5 - 1} - 1/{2 - sqrt3}`
`= sqrt3 - 1/{2 - sqrt3}`
`= {sqrt3cdot(2 - sqrt3)}/{2 - sqrt3} - 1/{2 - sqrt3}`
`= {sqrt3cdot(2 - sqrt3) - 1}/{2 - sqrt3}`
`= {2sqrt3 - 3 - 1}/{2 - sqrt3}`
`= {2sqrt3 - 4}/{2 - sqrt3}`
`= {- 4 + 2sqrt3}/{2 - sqrt3}`
`= {- 2cdot(2 - sqrt3)}/{2 - sqrt3}`
`= - 2`
Câu 11:
`A = sqrt{7 + 4sqrt3} - sqrt{7 - 4sqrt3}`
`= sqrt{4 + 4sqrt3 + 3} - sqrt{4 - 4sqrt3 + 3}`
`= sqrt{2^2 + 2cdot2cdot sqrt3 + (sqrt3)^2} - sqrt{2^2 - 2cdot2cdot sqrt3 + (sqrt3)^2}`
`= sqrt{(2 + sqrt3)^2} - sqrt{(2 - sqrt3)^2}`
`= |2 + sqrt3| - |2 - sqrt3|`
`= (2 + sqrt3) - (2 - sqrt3)` (Vì `2 = sqrt4 > sqrt3`)
`= 2 + sqrt3 - 2 + sqrt3`
`= (2 - 2) + (sqrt3 + sqrt3)`
`= 2sqrt3`
