Đáp án+Giải thích các bước giải:
1,
a,
`(2\sqrt{75}+2\sqrt{20}-2\sqrt{27}).2\sqrt{3}-3\sqrt{60}`
`=(10\sqrt{3}+4\sqrt{5}-6\sqrt{3}).2\sqrt{3}-6\sqrt{15}`
`=(4\sqrt{3}+4\sqrt{5}).2\sqrt{3}-6\sqrt{15}`
`=24+8\sqrt{15}-6\sqrt{15}`
`=24+2\sqrt{15}`
b,
`\frac{3+2\sqrt{3}}{\sqrt{3}}+\frac{2}{\sqrt{3}+1}-\sqrt{(6-5\sqrt{3})^2}`
`=\frac{\sqrt{3}(\sqrt{3}+2)}{\sqrt{3}}+\frac{2(\sqrt{3}-1)}{3-1}-|6-5\sqrt{3}|`
`=\sqrt{3}+2+\frac{2(\sqrt{3}-1)}{2}-(5\sqrt{3}-6)`
`=\sqrt{3}+2+\sqrt{3}-1-5\sqrt{3}+6`
`=7-3\sqrt{3}`
c,
`\sqrt{8-2\sqrt{15}}(\sqrt{5}+\sqrt{3})`
`=\sqrt{5-2.\sqrt{5}.\sqrt{3}+3}(\sqrt{5}+\sqrt{3})`
`=\sqrt{(\sqrt{5})^2-2.\sqrt{5}.\sqrt{3}+(\sqrt{3})^2}(\sqrt{5}+\sqrt{3})`
`=\sqrt{(\sqrt{5}-\sqrt{3})^2(\sqrt{5}+\sqrt{3})`
`=|\sqrt{5}-\sqrt{3}|(\sqrt{5}+\sqrt{3})`
`=(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})`
`=5-3`
`=2`
