Đáp án+Giải thích các bước giải:

 `VD3:`

`a)\sqrt{25.1,21}=\sqrt{5^{2}.(1,1)^{2}}=\sqrt{(5.1,1)^{2}}=5.1,1=5,5`

`b)\sqrt{369.90}=\sqrt{6^{2}.10.3^{2}.10}=\sqrt{(6.3)^{2}.10^{2}}`

`=\sqrt{18^{2}.10^{2}}=\sqrt{(18.10)^{2}}=18.10=180`

`VD4:`

`a)\sqrt{20}.\sqrt{5}=\sqrt{20.5}=\sqrt{100}=\sqrt{10^{2}}=10`

`b)\sqrt{2,8}.\sqrt{7}.\sqrt{10}=\sqrt{2,8.7.10}=\sqrt{28.7}=\sqrt{2^{2}.7.7}`

`=\sqrt{2^{2}.7^{2}}=\sqrt{(2.7)^{2}}=2.7=14`

`VD5:`

`a)\sqrt{3a}.\sqrt{27a}(a\ge0)`

`=\sqrt{3a.27.a}`

`=\sqrt{81a^{2}}`

`=\sqrt{(9a)^{2}}`

`=|9a|`

`=9a`

`b)\sqrt{8a.5ab.10b^{3}}`

`=\sqrt{400a^{2}b^{4}}`

`=\sqrt{(20ab^{2})^{2}}`

`=|20ab^{2}|`

`=20b^{2}|a|` (do `b^{2}\ge0AAb`)

`+)` Trương hợp `1` : Với `a\ge0` thì: `|a|=a` Khi đó ta được:

`20b^{2}a`

`+)` Trường hợp `2:` Với `a<0` thì: `|a|=-a` Khi đó ta được:

`20b^{2}.(-a)=-20b^{2}a`

`VD6:`

`a)\sqrt{75}=\sqrt{5^{2}.3}=5\sqrt{3}`

`b)-\sqrt{18}.\sqrt{24}=-\sqrt{3^{2}.2.2^{2}.6}`

`=-\sqrt{3^{2}.2^{3}.2.3}`

`=-\sqrt{3^{2}.16.3}`

`=-3.\sqrt{4^{2}.3}`

`=-3.4.\sqrt{3}`

`=-12\sqrt{3}`

`c)\sqrt{15a}.\sqrt{3a}(a>0)`

`=\sqrt{15a.3a}=\sqrt{5.3.3.a^{2}}`

`=\sqrt{(3a)^{2}}.\sqrt{5}`

`=|3a|.\sqrt{5}`

`=3a\sqrt{5}`

`VD7:`

`a)4\sqrt{3}=\sqrt{4^{2}.3}=\sqrt{16.3}=\sqrt{48}`

`b)-3\sqrt{6}=-\sqrt{3^{2}.6}=-\sqrt{9.6}=-\sqrt{54}`

`c)a\sqrt{2/a}(a>0)`

`=\sqrt{a^{2}. 2/a}`

`=\sqrt{\frac{2a.a}{a}}`

`=\sqrt{2a}`