Đáp án+Giải thích các bước giải:
a,
`\sqrt{12-2\sqrt{35}}+\sqrt{7-2\sqrt{10}}+\sqrt{2}`
`=\sqrt{7-2.\sqrt{7}.\sqrt{5}+5}+\sqrt{5-2.\sqrt{5}.\sqrt{2}+2}+\sqrt{2}`
`=\sqrt{(\sqrt{7}-\sqrt{5})^2}+\sqrt{(\sqrt{5}-\sqrt{2})^2}+\sqrt{2}`
`=\sqrt{7}-\sqrt{5}+\sqrt{5}-\sqrt{2}+\sqrt{2}`
`=\sqrt{7}`
b,
`\frac{4}{\sqrt{3}+1}+\frac{6}{\sqrt{3}-3}-\frac{5}{\sqrt{3}-2}`
`=\frac{4(\sqrt{3}-1)}{3-1}-\frac{6(3+\sqrt{3})}{9-3}+\frac{5(2+\sqrt{3})}{4-3}`
`=\frac{4(\sqrt{3}-1)}{2}-\frac{6(3+\sqrt{3})}{6}+\frac{5(2+\sqrt{3})}{1}`
`=2(\sqrt{3}-1)-(3+\sqrt{3})+5(2+\sqrt{3})`
`=2\sqrt{3}-2-3-\sqrt{3}+10+5\sqrt{3}`
`=6\sqrt{3}+5`
