Đáp án+Giải thích các bước giải:

 $\color{#a8b0b4}{⸻}\color{#91999d}{⸻}\color{#7a8286}{⸸}\color{#636b6f}{⛧}
\color{#4c5356}{𝕯}\color{#434a4d}{ψ}\color{#3b4244}{ภ}\color{#32393b}{ค}
\color{#2a3133}{๓}\color{#21282a}{๏}\color{#1a2123}{ภ}\color{#141a1c}{ร}
\color{#0f1516}{ฬ}\color{#0a1011}{๏}\color{#05090a}{ɭ}\color{#020406}{๔}
\color{#05090a}{⛧}\color{#0a1011}{⸸}\color{#141a1c}{⸻}\color{#1a2123}{⸻}$

Bài `1:`

`a)`

$(*)$

`\sqrt{5/12}=\frac{\sqrt{5}}{\sqrt{12}}=\frac{\sqrt{5}.\sqrt{12}}{(\sqrt{12})^{2}}=\frac{\sqrt{60}}{12}=\frac{\sqrt{2^{2}.15}}{12}=\frac{2\sqrt{15}}{2.6}=\frac{\sqrt{15}}{6}`

$(*)$

`\sqrt{17/50}=\frac{\sqrt{17}}{\sqrt{50}}=\frac{\sqrt{17}.\sqrt{50}}{(\sqrt{50})^{2}}=\frac{\sqrt{17.5^{2}.2}}{50}=\frac{5\sqrt{34}}{5.10}=\frac{\sqrt{34}}{10}`

`b)`

$(*)$

`\frac{12}{3-\sqrt{3}}=\frac{12.(3+\sqrt{3})}{(3-\sqrt{3}).(3+\sqrt{3})}`

`=\frac{12.(3+\sqrt{3})}{3^{2}-(\sqrt{3})^{2}}`

`=\frac{12.(3+\sqrt{3})}{6}`

`=2.(3+\sqrt{3})`

`=6+2\sqrt{3}`

$(*)$

`\frac{8}{\sqrt{5}+2}=\frac{8.(\sqrt{5}-2)}{(\sqrt{5}+2).(\sqrt{5}-2)}`

`=\frac{8.(\sqrt{5}-2)}{(\sqrt{5})^{2}-2^{2}}`

`=\frac{8.(\sqrt{5}-2)}{1}`

`=8\sqrt{5}-16`

`c)`

$(*)$

`\frac{14}{\sqrt{10}+\sqrt{3}}=\frac{14.(\sqrt{10}-\sqrt{3})}{(\sqrt{10}+\sqrt{3}).(\sqrt{10}-\sqrt{3})}`

`=\frac{14.(\sqrt{10}-\sqrt{3})}{(\sqrt{10})^{2}-(\sqrt{3})^{2}}`

`=\frac{14.(\sqrt{10}-\sqrt{3})}{7}`

`=2.(\sqrt{10}-\sqrt{3})`

`=2\sqrt{10}-2\sqrt{3}`

$(*)$

`\frac{2}{\sqrt{b}-\sqrt{5}}` `(b\ge0;b\ne5)`

`=\frac{2.(\sqrt{b}+\sqrt{5})}{(\sqrt{b}-\sqrt{5}).(\sqrt{b}+\sqrt{5})}`

`=\frac{2\sqrt{b}+2\sqrt{5}}{(\sqrt{b})^{2}-(\sqrt{5})^{2}}`

`=\frac{2\sqrt{b}+2\sqrt{5}}{b-5}`

Bài `2:`

`a)(5\sqrt{2}+\sqrt{8}).2\sqrt{2}`

`=5\sqrt{2}.2\sqrt{2}+\sqrt{2^{2}.2}.2\sqrt{2}`

`=10\sqrt{2^{2}}+2\sqrt{2}.2\sqrt{2}`

`=10.2+(2\sqrt{2})^{2}`

`=20+2^{2}.2`

`=20+4.2`

`=28`

`b)\sqrt{75}+2\sqrt{48}-\sqrt{300}`

`=\sqrt{5^{2}.3}+2.\sqrt{4^{2}.3}-\sqrt{10^{2}.3}`

`=5\sqrt{3}+2.4\sqrt{3}-10\sqrt{3}`

`=-5\sqrt{3}+8\sqrt{3}`

`=3\sqrt{3}`

`c)\sqrt{16}.\sqrt{25}+\sqrt{196}:\sqrt{49}`

`=\sqrt{4^{2}}.\sqrt{5^{2}}+\sqrt{14^{2}}:\sqrt{7^{2}}`

`=4.5+14:7`

`=20+2`

`=22`

`d)\frac{1}{2+\sqrt{3}}-\frac{1}{2-\sqrt{3}}`

`=\frac{1.(2-\sqrt{3})}{(2-\sqrt{3}).(2+\sqrt{3})}-\frac{2+\sqrt{3}}{(2-\sqrt{3}).(2+\sqrt{3})}`

`=\frac{2-\sqrt{3}-2-\sqrt{3}}{(2-\sqrt{3}).(2+\sqrt{3})^{2}}`

`=\frac{-2\sqrt{3}}{2^{2}-(\sqrt{3})^{2}}`

`=\frac{-2\sqrt{3}}{1}`

`=-2\sqrt{3}`