Đáp án+Giải thích các bước giải:
a,
`\sqrt{(\sqrt{2}-1)^2}-\sqrt{(\sqrt{2}+1)^2}`
`=|\sqrt{2}-1|-|\sqrt{2}+1|`
`=\sqrt{2}-1-(\sqrt{2}+1)`
`=\sqrt{2}-1-\sqrt{2}-1`
`=-2`
b,
`\sqrt{(1+\sqrt{3})^2}-\sqrt{(\sqrt{2}-\sqrt{3})^2}-\sqrt{(1+\sqrt{2})^2}`
`=|1+\sqrt{3}|-|\sqrt{2}-\sqrt{3}|-|1+\sqrt{2}|`
`=1+\sqrt{3}-(\sqrt{3}-\sqrt{2})-(1+\sqrt{2})`
`=1+\sqrt{3}-\sqrt{3}+\sqrt{2}-1-\sqrt{2}`
`=0`
c,
`\sqrt{4-2\sqrt{3}}+\sqrt{3}`
`=\sqrt{3-2.\sqrt{3}.1+1}+\sqrt{3}`
`=\sqrt{(\sqrt{3})^2-2.\sqrt{3}.1+1^2}+\sqrt{3}`
`=\sqrt{(\sqrt{3}-1)^2}+\sqrt{3}`
`=|\sqrt{3}-1|+\sqrt{3}`
`=\sqrt{3}-1+\sqrt{3}`
`=2\sqrt{3}-1`
d,
`\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}`
`=\sqrt{5+2.\sqrt{5}.2+4}-\sqrt{5-2.\sqrt{5}.2+4}`
`=\sqrt{(\sqrt{5})^2+2.\sqrt{5}.2+2^2}-\sqrt{(\sqrt{5})^2-2.\sqrt{5}.2+2^2}`
`=\sqrt{(\sqrt{5}+2)^2}-\sqrt{(\sqrt{5}-2)^2}`
`=|\sqrt{5}+2|-|\sqrt{5}-2|`
`=\sqrt{5}+2-(\sqrt{5}-2)`
`=\sqrt{5}+2-\sqrt{5}+2`
`=4`
