Hướng dẫn trả lời:
b) `sqrt{7 - 2sqrt{10}} - sqrt{7 + 2sqrt{10}}`
`= sqrt{5 - 2sqrt{10} + 2} - sqrt{5 + 2sqrt{10} + 2}`
`= sqrt{(sqrt{5})^2 - 2*sqrt{5}*sqrt{2} + (sqrt{2})^2} - sqrt{(sqrt{5})^2 + 2*sqrt{5}*sqrt{2} + (sqrt{2})^2}`
`= sqrt{(sqrt{5} - sqrt{2})^2} - sqrt{(sqrt{5} + sqrt{2})^2}`
`= |sqrt{5} - sqrt{2}| - |sqrt{5} + sqrt{2}|`
`= (sqrt{5} - sqrt{2}) - (sqrt{5} + sqrt{2})` (Vì `sqrt{5} > sqrt{2}`)
`= sqrt{5} - sqrt{2} - sqrt{5} - sqrt{2}`
`= (sqrt{5} - sqrt{5}) + (- sqrt{2} - sqrt{2})`
`= - 2sqrt{2}`
e) `sqrt{17 - 12sqrt{2}} + sqrt{9 + 4sqrt{2}}`
`= sqrt{9 - 12sqrt{2} + 8} + sqrt{8 + 4sqrt{2} + 1}`
`= sqrt{3^2 - 2*3*2sqrt{2} + (2sqrt{2})^2} + sqrt{(2sqrt{2})^2 + 2*2sqrt{2}*1 + 1^2}`
`= sqrt{(3 - 2sqrt{2})^2} + sqrt{(2sqrt{2} + 1)^2}`
`= |3 - 2sqrt{2}| + |2sqrt{2} + 1|`
`= (3 - 2sqrt{2}) + (2sqrt{2} + 1)`
`= 3 - 2sqrt{2} + 2sqrt{2} + 1`
`= (3 + 1) + (- 2sqrt{2} + 2sqrt{2})`
`= 4`
Đáp án:
b) `= - 2sqrt{2}`
e) `= 4`
