Hướng dẫn trả lời:
`(sqrt{18} + sqrt{0,5} - 3cdot sqrt{1/3}) - (sqrt{1/8} - sqrt{75})`
`= (sqrt{9cdot2} + sqrt{1/2} - sqrt{3^2cdot1/3}) - (sqrt{1/2^3} - sqrt{25cdot3})`
`= (sqrt{3^2cdot2} + sqrt{2/4} - sqrt{9cdot1/3}) - (sqrt{2/2^4} - sqrt{5^2cdot3})`
`= (3sqrt{2} + sqrt{2/2^2} - sqrt{3}) - (sqrt{2/(2^2)^2} - 5sqrt{3})`
`= (3sqrt{2} + sqrt{2}/2 - sqrt{3}) - (sqrt{2}/4 - 5sqrt{3})`
`= 3sqrt{2} + sqrt{2}/2 - sqrt{3} - sqrt{2}/4 + 5sqrt{3}`
`= 3sqrt{2} + (sqrt{2}/2 - sqrt{2}/4) + (- sqrt{3} + 5sqrt{3})`
`= 3sqrt{2} + ({2sqrt{2}}/4 - sqrt{2}/4) + 4sqrt{3}`
`= 3sqrt{2} + sqrt{2}/{4} + 4sqrt{3}`
`= {12sqrt{2}}/4 + sqrt{2}/{4} + 4sqrt{3}`
`= {13sqrt{2}}/4 + {16sqrt{3}}/4`
`= {13sqrt{2} + 16sqrt{3}}/4`
Đáp án:
`= {13sqrt{2} + 16sqrt{3}}/4`
