Đáp án:
`\root{3}{7+5\sqrt{2}}-\root{3}{7-5\sqrt{2}}=2\sqrt{2}`
Giải thích các bước giải:
`\root{3}{7+5\sqrt{2}}-\root{3}{7-5\sqrt{2}}`
`=\root{3}{1+3*1*\sqrt{2}+3*2*1+2\sqrt{2}}-\root{3}{1-3*1*\sqrt{2}+3*2*1-2\sqrt{2}}`
`=\root{3}{(1+\sqrt{2})^3}-\root{3}{(1-\sqrt{2})^3}`
`=1+\sqrt{2}-(1-\sqrt{2})`
`=1+\sqrt{2}-1+\sqrt{2}`
`=2\sqrt{2}`