Lời giải
`1)` Đặt `A=\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}`
`A=\sqrt{8+5-\sqrt{4.8.5}}-\sqrt{45+8+2.2.\sqrt{2.45}}`
`A=\sqrt{(\sqrt{8})^2-2.\sqrt{8}.\sqrt{5}+(\sqrt{5})^2}-\sqrt{(\sqrt{45})^2+2.2.\sqrt{2}.\sqrt{45}+(\sqrt{8})^2}`
`A=\sqrt{(\sqrt{8}-\sqrt{5})^2}-\sqrt{(\sqrt{45}+\sqrt{8})^2}`
`A=\sqrt{8}-\sqrt{5}-(\sqrt{45}+\sqrt{8})`
`A=\sqrt{8}-\sqrt{5}-\sqrt{45}-\sqrt{8}`
`A=-\sqrt{5}-\sqrt{45}`
`A=-\sqrt{5}-\sqrt{9.5}`
`A=-\sqrt{5}-3\sqrt{5}`
`A=-4\sqrt{5}.`
`2)` Đặt `B=\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}`
`=>B^2=3-\sqrt{5}+2.\sqrt{3-\sqrt{5}}.\sqrt{3+\sqrt{5}}+3+\sqrt{5}`
`B^2=6+2.\sqrt{(3-\sqrt{5})(3+\sqrt{5})}`
`B^2=6+2.\sqrt{3^2-(\sqrt{5})^2}`
`B^2=6+2.\sqrt{9-5}`
`B^2=6+2.\sqrt{4}`
`B^2=6+2.2`
`B^2=10`
`=>B=\sqrt{10}.`
