84~105题:根据原始照片1000195308.jpg重新抄题。第93题根号层级尚待核对;其他题为新计算稿,仍建议与原图对照。分式视觉排版尚待完善。
(84) (2¼)1/3 × 361/3 + (−9)1/3 × (⅓)−2/3
=(81)1/3 + (−9)1/3×91/3
=∛81 − ∛81
=0
(85) ∛125 + ∛(−1000) + √(−¾)²
=5−10+¾
=−17/4
(86) √[−(1/27)−1/3+(√19)²]
=√(−3+19)
=4
(87) 2√2 + √5/2 − 10√0.04
=2√2+√5/2−2
(88) (8/27)1/3−√(−2)²+(−0.5)−3÷163/4+(1/(√2−1))0
=2/3−2−8÷8+1
=−4/3
(89) |√2−√3|+2√2
=√3−√2+2√2
=√3+√2
(90) (−2)³×√(−4)²+∛(−4)³×(−½)²−∛27
=−8×4−4×¼−3
=−36
(91) (2 7/9)1/2+(−1)²+(2 10/27)−2/3
=5/3+1+(64/27)−2/3
=8/3+9/16
=155/48
(92) (2¼)1/3×361/3+(−9)1/3×(⅓)−2/3
=∛81−∛81
=0
(93) √(2+√3)·√(2+√(2+√3))·√(2+√(2+√(2+√3)))·√(2−√(2+√(2+√(2+√3))))
=原题为连乘嵌套根式;需要进一步核对最后一项的根号层级
(94) (2 7/9)1/2+(√3)⁹÷(√3)⁷
=5/3+(√3)²
=14/3
(95) (√5)⁰+(21/2×81/2)−(⅓)−2
=1+4−9
=−4
(96) (∛3×√3)⁶
=3(1/3+1/2)×6
=3⁵
=243
(97) ⁶√(4²)×√8÷⁶√2
=24/6+3/2−1/6
=4
(98) (12³×4³)1/6
=481/2
=4√3
(99) ∛6÷∛2×¹²√3
=∛3×¹²√3
=35/12
(100) ∛0.125−√(3/16)+∛(1−⅛)²
=½−√3/4+∛(49/64)
=½−√3/4+∛49/4
(101) √6−(2√3−(3/2)√3)·√2+(√2+√3)²
=√6−½√6+5+2√6
=5+(5/2)√6
(102) √(√2−√3)²+|√3−2|+|2√2−3|+√(3−2√2)
=√3−√2+2−√3+3−2√2+√2−1
=4−2√2
(103) √(−3)²+(√7)²+(3−2√3)⁰÷√3
=3+7+1/√3
=10+√3/3
(104) 91/3×271/2÷31/6
=32/3+3/2−1/6
=9