Đáp án:
`F=\sqrt{1+3\sqrt{2}}`
`G=\sqrt{5}`
`H=\sqrt{3}+1`
`I=3\sqrt{2}+1`
Giải thích các bước giải:
Ta có:
`F=\sqrt{3+2\sqrt{2}-\sqrt{6-4\sqrt{2}}}`
`=\sqrt{3+2\sqrt{2}-2+\sqrt{2}}`
`=\sqrt{1+3\sqrt{2}}`
`G=2+\sqrt{17+4\sqrt{9+4\sqrt{5}}}`
`=2+\sqrt{17-4(2+\sqrt{5})}`
`=2+\sqrt{17-8-4\sqrt{5}}`
`=2+\sqrt{9-4\sqrt{5}}`
`=2+\sqrt{5}-2`
`=\sqrt{5}`
`H=\sqrt{\sqrt{2}+2\sqrt{3}+\sqrt{18-8\sqrt{2}}}`
`=\sqrt{\sqrt{2}+2\sqrt{3}+4-\sqrt{2}}`
`=\sqrt{2\sqrt{3}+4}`
`=\sqrt{3}+1`
`I=\sqrt{13+6\sqrt{4+\sqrt{9-4\sqrt{2}}}}`
`=\sqrt{13+6\sqrt{4+\frac{4-\sqrt{2}}{\sqrt{2}}}}`
`=\sqrt{13+6+6\sqrt{2}}`
`=\sqrt{19+6\sqrt{2}}`
`=3\sqrt{2}+1`
