`1,`

`a)` Có: `3\sqrt{5}=\sqrt{9.5}=\sqrt{45}`

`2\sqrt{6}=\sqrt{4.6}=\sqrt{24}`

`4\sqrt{2}=\sqrt{16.2}=\sqrt{32}`

Do `24<29<32<45`

`=> 2\sqrt{6}<\sqrt{19}<4\sqrt{2}<3\sqrt{5}`

`b) 6\sqrt{2}=\sqrt{36.2}=\sqrt{72}`

`3\sqrt{7}=\sqrt{9.7}=\sqrt{63}`

`2\sqrt{14}=\sqrt{4.14}=\sqrt{56}`

Do `38<56<63<72`

`=> \sqrt{38}<2\sqrt{14}<3\sqrt{7}<6\sqrt{2}`

`2,`

`a) ab+b\sqrt{a}+\sqrt{a}+1`

`=\sqrt{a}b(\sqrt{a}+1)+(\sqrt{a}+1)`

`=(\sqrt{a}+1)(\sqrt{a}b+1)`

`b) \sqrt{x^3}-\sqrt{y^3}+\sqrt{x^2y}-\sqrt{xy^2}`

`=(\sqrt{x}-\sqrt{y})(x+\sqrt{xy}+y)+\sqrt{xy}(\sqrt{x}-\sqrt{y})`

`=(\sqrt{x}-\sqrt{y})(x+2\sqrt{xy}+y)`

`=(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})^2`

Đáp án:

Giải thích các bước giải:

   `text{Bài 1}`

`a)` `text{ta xét các bình phương}`

`+ ) (3sqrt(5))^2=45`

`+) (2sqrt(6))^2=24`

`+) (sqrt(29))^2=29`

`+) (4sqrt(2))^2=32`

`text{ta có}`  `24<29<32<45`

        `<=>2sqrt(6)<sqrt(29)<4sqrt(2)<3sqrt(5)`

`text{vậy sắp xếp theo thứ tự tăng dàn là}` 

     `2sqrt(6);sqrt(29);4sqrt(2);3sqrt(5)`

 `b)

`a)` `text{ta xét các bình phương}`

`+ ) (6sqrt(2))^2=72`

`+) (sqrt(38))^2=38`

`+) (3sqrt(7))^2=63`

`+) (2sqrt(14))^2=56`

`text{ta có}`  `38<56<63<72`

        `<=>sqrt(38)<2sqrt(14)<3sqrt(7)<6sqrt(2)`

`text{vậy sắp xếp theo thứ tự tăng dàn là}` 

     `sqrt(38);2sqrt(14);3sqrt(7);6sqrt(2)`

   `text{Bài 2}`

`a) ab+bsqrt(a)+sqrt(a)+1`

`=bsqrt(a)(sqrt(a)+1)+(sqrt(a)+1)`

`=(sqrt(a)+1)(bsqrt(a)+1)`

 `b) sqrt(x^3)-sqrt(y^3)+sqrt(x^2y)-sqrt(xy^2)`

`=(sqrt(x)^3-sqrt(y)^3)+(sqrt(x)^2sqrt(y)-sqrt(x)sqrt(y)^2)`

`=(sqrt(x)-sqrt(y))(x+sqrt(xy)+y)+sqrt(xy)(sqrt(x)-sqrt(y))`

`=(sqrt(x)-sqrt(y))(sqrt(x)^2+2sqrt(xy)+sqrt(y)^2)`

`=(sqrt(x)-sqrt(y))(sqrt(x)+sqrt(y))^2`

`text{xin 5 sao và hay nhất nha}`