[2sin50+sin10(1+根号3tan10）]×根号（2sin²80）

[2sin50°+sin10°(1+√3tan10°)]•√(2sin²80°) = [2sin50 + sin10(cos10+√3sin10)/cos10]•√2sin80 = [2sin50cos10+2sin10(cos60cos10+sin60sin10)•√2sin80/cos10 = 2[sin50cos10 + sin10cos(60-10)]•√2 = 2sin(50+10)•√2 = √6