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1463
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10235
8212
Đáp án:
`a) 2sqrt{28} + 2sqrt{63} - 3sqrt{175} + sqrt{112} - sqrt{20}`
` = 2sqrt{4. 7} + 2sqrt{9 . 7} - 3sqrt{25 . 7} + sqrt{16 . 7} - sqrt{20}`
` = 2 . 2sqrt{7} + 2 . 3sqrt{7} - 3 . 5sqrt{7} + 4sqrt{7} - sqrt{20}`
` = 4sqrt{7} + 6sqrt{7} - 15sqrt{7} + 4sqrt{7} - sqrt{20}`
` = -sqrt{7} - sqrt{20}`
`b) sqrt{2 + sqrt{3}} + sqrt{2 - sqrt{3}}`
` = 1/(sqrt{2}) . ( sqrt{4 + 2sqrt{3}} + sqrt{4 - 2sqrt{3}})`
` = 1/(sqrt{2}) . (sqrt{3 + 2sqrt{3} + 1} + sqrt{3 - 2sqrt{3} + 1})`
` = 1/(sqrt{2}) . ( sqrt{ (sqrt{3} + 1)^2} + sqrt{ (sqrt{3} - 1)^2})`
` = 1/(sqrt{2}) . (|sqrt{3} + 1| + |sqrt{3} - 1|)`
` = 1/(sqrt{2}) . (sqrt{3} + 1 + sqrt{3} - 1)`
` = 1/(sqrt{2}) . (2sqrt{3})`
` = sqrt{6}`
`c) 2/(3 +2sqrt{2}) - 2/(3 - 2sqrt{2})`
` = ( 2(3 - 2sqrt{2}) - 2(3 + 2sqrt{2}))/((3+2sqrt{2})(3-2sqrt{2}))`
` = (6 - 4sqrt{2} - 6 - 4sqrt{2})/(9 - 8)`
` = -8sqrt{2}`
`d) ( (2sqrt{2} + 3sqrt{3})/(sqrt{2} + sqrt{3}) - sqrt{6}) : (sqrt{2} - sqrt{3}) - (2sqrt{6})/(sqrt{2} + sqrt{3})`
` = ( sqrt{12} + sqrt{27} - sqrt{6} . sqrt{2} - sqrt{6} . sqrt{3})/(sqrt{2} + sqrt{3}) : (sqrt{2} - sqrt{3}) - (2sqrt{6})/(sqrt{2} + sqrt{3})`
` = (sqrt{27} - sqrt{18})/(sqrt{2} + sqrt{3}) : (sqrt{2} - sqrt{3}) - (2sqrt{6})/(sqrt{2} + sqrt{3})`
` = ( 3 . (sqrt{3} - sqrt{2}) )/(sqrt{2} + sqrt{3}) : (sqrt{2} - sqrt{3}) - (2sqrt{6})/(sqrt{2} + sqrt{3})`
` = -3/(sqrt{2} + sqrt{3}) - (2sqrt{6})/(sqrt{2} + sqrt{3})`
` = (-3 - 2sqrt{6})/(sqrt{2} + sqrt{3})`
` = ( (-3 - 2sqrt{6})(sqrt{3} - 2))/((sqrt{3} - sqrt{2})(sqrt{3} + sqrt{2}))`
` = (-3sqrt{3} + 6 - 2sqrt{18} + 4sqrt{6})/(3 - 2)`
` = -3sqrt{3} + 6 - 2 . 3sqrt{2} + 4sqrt{6}`
` = -9sqrt{3} + 6 + 4sqrt{6}`
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