Đáp án:
`a)` `18`
`b)` `4`
Giải thích các bước giải:
`1)` `3\sqrt{45}+\sqrt{(2-\sqrt{5})^2}-{10}/{\sqrt{5}+2}`
`=3\sqrt{3^2 .5}+|2-\sqrt{5}|-{10.(\sqrt{5}-2)}/{(\sqrt{5}+2)(\sqrt{5}-2)}`
`=3.3\sqrt{5}+\sqrt{5}-2-{10\sqrt{5}-20}/{5-2^2}`
`=9\sqrt{5}+\sqrt{5}-2-10\sqrt{5}+20`
`=(9+1-10).\sqrt{5}-2+20=18`
Vậy: `3\sqrt{45}+\sqrt{(2-\sqrt{5})^2}-{10}/{\sqrt{5}+2}=18`
$\\$
`b)` `({\sqrt{15}-\sqrt{10}}/{\sqrt{3}-\sqrt{2}}-4/{\sqrt{5}-1}+{3\sqrt{5}+5}/{\sqrt{5}+3}).(\sqrt{5}+1)`
`=({\sqrt{5}(\sqrt{3}-\sqrt{2})}/{\sqrt{3}-\sqrt{2}}-{4(\sqrt{5}+1)}/{(\sqrt{5}-1)(\sqrt{5}+1)}+{\sqrt{5}(3+\sqrt{5})}/{\sqrt{5}+3})(\sqrt{5}+1)`
`=(\sqrt{5}-{4(\sqrt{5}+1)}/{5-1^2}+\sqrt{5}).(\sqrt{5}+1)`
`=[2\sqrt{5}-(\sqrt{5}+1)].(\sqrt{5}+1)`
`=(\sqrt{5}-1)(\sqrt{5}+1)=5-1^2=4`
Vậy: `({\sqrt{15}-\sqrt{10}}/{\sqrt{3}-\sqrt{2}}-4/{\sqrt{5}-1}+{3\sqrt{5}+5}/{\sqrt{5}+3}).(\sqrt{5}+1)=4`
