Đáp án:
`\sqrt{8\sqrt{3}+8\sqrt{2}-\sqrt{15}-\sqrt{10}}`
Hoặc:
`8\sqrt{3}+8\sqrt{2}-\sqrt{15}-\sqrt{10}`
Giải thích các bước giải:
`\sqrt{\frac{8-\sqrt{5}}{\sqrt{3}-\sqrt{2}}}`
`= \sqrt{(8-\sqrt{5})(\sqrt{3}+\sqrt{2})}`
`= \sqrt{8\sqrt{3}+8\sqrt{2}-\sqrt{15}-\sqrt{10}}`
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`\frac{8-\sqrt{5}}{\sqrt{3}-\sqrt{2}}`
`= \frac{8-\sqrt{5}}{\sqrt{3}-\sqrt{2}}.\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}`
`= \frac{(8-\sqrt{5})(\sqrt{3-\sqrt{2}})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2})}`
`= \frac{(8-\sqrt{5})(\sqrt{3}+\sqrt{2})}{3-2}`
`= \frac{(8-\sqrt{5})(\sqrt{3}+\sqrt{2})}{1}`
`= (8-\sqrt{5})(\sqrt{3}+\sqrt{2})`
`= 8\sqrt{3}+8\sqrt{2}-\sqrt{15}-\sqrt{10}`