rút gọn biểu thức: a) (2√3+√5)√3 -√60 b)(5√2+2√5)√5 -√250 c) (√28-√12-√7)√7 +2√21 d) (√99-√18-√11)√11+3√22

Đáp án+Giải thích các bước giải:

`a) `

`(2sqrt{3} + sqrt{5})sqrt{3} - sqrt{60}`

`= 2sqrt{3}sqrt{3} + sqrt{5}sqrt{3} - sqrt{60} `

`= 23 + sqrt{15} - sqrt{60}`

`= 6 + sqrt{15} - sqrt{415} `

`= 6 + sqrt{15} - 2sqrt{15} `

`= 6 - sqrt{15} `

`b)`

`(5sqrt{2}+2sqrt{5})sqrt{5} - sqrt{250} `

`= 5sqrt{2}sqrt{5} + 2sqrt{5}sqrt{5} - sqrt{250} `

`= 5sqrt{10} + 25 - sqrt{2510}`

`= 5sqrt{10} + 10 - 5sqrt{10} `

`= 10 `

`c) `

`(sqrt{28} - sqrt{12} - sqrt{7})sqrt{7} + 2sqrt{21}`

`= sqrt{28}*sqrt{7} - sqrt{12}*sqrt{7} - sqrt{7}sqrt{7} + 2sqrt{21} `

`= sqrt{196} - sqrt{84} - 7 + 2sqrt{21} `

`= 14 - sqrt{84} - 7 + 2sqrt{21} `

`= 7 - sqrt{421} + 2sqrt{21} `

`= 7 - 2sqrt{21} + 2sqrt{21} `

`= 7`

`d) `

`(sqrt{99} - sqrt{18} - sqrt{11})sqrt{11} + 3sqrt{22}`

`= sqrt{99}*sqrt{11} - sqrt{18}*sqrt{11} - sqrt{11}sqrt{11} + 3sqrt{22} `

`= sqrt{1089} - sqrt{198} - 11 + 3sqrt{22} `

`= 33 - sqrt{198} - 11 + 3sqrt{22} `

`= 22 - sqrt{922} + 3sqrt{22} `

`= 22 - 3sqrt{22} + 3sqrt{22}`

`= 22`