All 100 targets have a solution.
\(1 = \frac{ 54 }{ 6 } - 8 \)
\(2 = \frac{ \frac{ 6! }{ 45 } }{ 8 }\)
\(3 = 6 \cdot 8 - 45 \)
\(4 = \frac{ 56 - 4! }{ 8 }\)
\(5 = 8 - \sqrt{\frac{ 54 }{ 6 }}\)
\(6 = 64 - 58 \)
\(7 = \sqrt{46 - 5 + 8 }\)
\(8 = 56 - 48 \)
\(9 = \frac{ 58 - 4 }{ 6 }\)
\(10 = \frac{ 6! }{ 48 } - 5 \)
\(11 = \frac{ 56 }{ 8 } + 4 \)
\(12 = 58 - 46 \)
\(13 = \frac{ 48 }{ 6 } + 5 \)
\(14 = 68 - 54 \)
\(15 = \frac{ 5! }{ \frac{ 48 }{ 6 } }\)
\(16 = \frac{ 56 + 8 }{ 4 }\)
\(17 = 65 - 48 \)
\(18 = 48 - 5 \cdot 6 \)
\(19 = 84 - 65 \)
\(20 = \frac{ 6! }{ 48 } + 5 \)
\(21 = 85 - 64 \)
\(22 = \frac{ 56 }{ 4 } + 8 \)
\(23 = 68 - 45 \)
\(24 = 56 - 4 \cdot 8 \)
\(25 = 5^{4 + 6 - 8 }\)
\(26 = \sqrt{54 \cdot 6} + 8 \)
\(27 = \frac{ 54 }{ 8 - 6 }\)
\(28 = 84 - 56 \)
\(29 = \sqrt{846 - 5 }\)
\(30 = 5! - 84 - 6 \)
\(31 = 45 - 6 - 8 \)
\(32 = 86 - 54 \)
\(33 = 46 - 5 - 8 \)
\(34 = 58 - 4 \cdot 6 \)
\(35 = \frac{ 58 }{ \sqrt{4} } + 6 \)
\(36 = \frac{ 6! }{ 8 } - 54 \)
\(37 = 48 - 5 - 6 \)
\(38 = 68 - \frac{ 5! }{ 4 }\)
\(39 = 85 - 46 \)
\(40 = \frac{ 48 \cdot 5 }{ 6 }\)
\(41 = 86 - 45 \)
\(42 = 5! - 84 + 6 \)
\(43 = 45 + 6 - 8 \)
\(44 = 56 - 4 - 8 \)
\(45 = \sqrt{45^{8 - 6 }}\)
\(46 = 56 - \sqrt{4} - 8 \)
\(47 = 45 - 6 + 8 \)
\(48 = ( 6 - 5 ) \cdot 48 \)
\(49 = 46 - 5 + 8 \)
\(50 = 58 - \sqrt{64 }\)
\(51 = 64 - 5 - 8 \)
\(52 = 54 + 6 - 8 \)
\(53 = 65 - 4 - 8 \)
\(54 = 56 - \frac{ 8 }{ 4 }\)
\(55 = 58 - \frac{ 6 }{ \sqrt{4 } }\)
\(56 = 54 - 6 + 8 \)
\(57 = \frac{ 456 }{ 8 }\)
\(58 = \frac{ 8 }{ 4 } + 56 \)
\(59 = 45 + 6 + 8 \)
\(60 = \frac{ 45 \cdot 8 }{ 6 }\)
\(61 = 64 + 5 - 8 \)
\(62 = 56 - \sqrt{4} + 8 \)
\(63 = 65 - \frac{ 8 }{ 4 }\)
\(64 = 5! - 64 + 8 \)
\(65 = \sqrt{65^{\frac{ 8 }{ 4 }}}\)
\(66 = 58 + \sqrt{64 }\)
\(67 = 64 - 5 + 8 \)
\(68 = 54 + 6 + 8 \)
\(69 = 65 - 4 + 8 \)
\(70 = \frac{ 84 \cdot 5 }{ 6 }\)
\(71 = 65 - \sqrt{4} + 8 \)
\(72 = \frac{ 54 }{ 6 } \cdot 8 \)
\(73 = 84 - 5 - 6 \)
\(74 = ( 6 + 8 ) \cdot 5 + 4 \)
\(75 = 85 - 4 - 6 \)
\(76 = 58 + 4! - 6 \)
\(77 = 85 - \sqrt{64 }\)
\(78 = 5 \cdot 6 + 48 \)
\(79 = \frac{ 5! }{ 8 } + 64 \)
\(80 = ( 8 - 4 )! + 56 \)
\(81 = 65 + 4! - 8 \)
\(82 = 4 \cdot 6 + 58 \)
\(83 = 84 + 5 - 6 \)
\(84 = ( 6 - 5 ) \cdot 84 \)
\(85 = \frac{ 68 }{ 4 } \cdot 5 \)
\(86 = 5 \cdot 8 + 46 \)
\(87 = \frac{ 58 \cdot 6 }{ 4 }\)
\(88 = 4 \cdot 8 + 56 \)
\(89 = ( 8 - 4 )! + 65 \)
\(90 = ( 8 - 6 ) \cdot 45 \)
\(91 = \sqrt{85^{\sqrt{4}}} + 6 \)
\(92 = ( 5 + 6 ) \cdot 8 + 4 \)
\(93 = \sqrt{64} + 85 \)
\(94 = 6^{\sqrt{4}} + 58 \)
\(95 = 84 + 5 + 6 \)
\(96 = \frac{ 6! }{ 5 } - 48 \)
\(97 = 4 \cdot 8 + 65 \)
\(98 = \frac{ 5! }{ 4 } + 68 \)
\(99 = \frac{ 6! }{ 8 } + 4 + 5 \)
\(100 = \sqrt{4}^{5} + 68 \)