Hướng dẫn trả lời:
Bài 3:
1) `sqrt{50} - 2sqrt{20} + 4sqrt{180}`
`= sqrt{25cdot2} - 2sqrt{4cdot5} + 4sqrt{36cdot5}`
`= sqrt{5^2cdot2} - 2sqrt{2^2cdot5} + 4sqrt{6^2cdot5}`
`= 5sqrt{2} - 2cdot2sqrt{5} + 4cdot6sqrt{5}`
`= 5sqrt{2} - 4sqrt{5} + 24sqrt{5}`
`= (- 4sqrt{5} + 24sqrt{5}) + 5sqrt{2}`
`= 20sqrt{5} + 5sqrt{2}`
2) `3sqrt{2/9} - 6sqrt{3/4} + sqrt{27} - sqrt{2}`
`= sqrt{3^2cdot2/9} - sqrt{6^2cdot3/4} + sqrt{3^3} - sqrt{2}`
`= sqrt{9cdot2/9} - sqrt{36cdot3/4} + sqrt{3^3} - sqrt{2}`
`= sqrt{2} - sqrt{27} + 3sqrt{3} - sqrt{2}`
`= sqrt{2} - sqrt{3^3} + 3sqrt{3} - sqrt{2}`
`= sqrt{2} - 3sqrt{3} + 3sqrt{3} - sqrt{2}`
`= (- 3sqrt{3} + 3sqrt{3}) + (sqrt{2} - sqrt{2})`
`= 0`
3) `(sqrt{28} - 2sqrt{3} + sqrt{7})cdot sqrt{7} + sqrt{8}`
`= (sqrt{4cdot7} - 2sqrt{3} + sqrt{7})cdot sqrt{7} + sqrt{8}`
`= (2sqrt{7} - 2sqrt{3} + sqrt{7})cdot sqrt{7} + sqrt{8}`
`= [(2sqrt{7} + sqrt{7}) - 2sqrt{3}]cdot sqrt{7} + sqrt{8}`
`= (3sqrt{7} - 2sqrt{3})cdot sqrt{7} + sqrt{8}`
`= 3sqrt{7}cdot sqrt{7} - 2sqrt{3}cdot sqrt{7} + sqrt{2^3}`
`= 3cdot7 - 2sqrt{21} + 2sqrt{2}`
`= 21 - 2sqrt{21} + 2sqrt{2}`
4) `(sqrt{6} + sqrt{5})^2 - sqrt{120}`
`= (sqrt{6})^2 + 2cdot sqrt{6}cdot sqrt{5} + (sqrt{5})^2 - sqrt{4cdot30}`
`= 6 + 2sqrt{30} + 5 - 2sqrt{30}`
`= (6 + 5) + (2sqrt{30} - 2sqrt{30})`
`= 11 + 0`
`= 11`
Giải thích:
Áp dụng HĐT `(A + B)^2 = A^2 + 2AB + B^2`
