All 100 targets have a solution.
\(1 = ( ( 5 - 4 )^{7} )^{8 }\)
\(2 = 7 \cdot 8 - 54 \)
\(3 = \sqrt{57 - 48 }\)
\(4 = \sqrt{74 - 58 }\)
\(5 = \sqrt{57 - 4 \cdot 8 }\)
\(6 = \sqrt{57 - 48 }!\)
\(7 = 47 - 5 \cdot 8 \)
\(8 = \frac{ 58 - \sqrt{4} }{ 7 }\)
\(9 = 57 - 48 \)
\(10 = \frac{ 5! }{ \frac{ 84 }{ 7 } }\)
\(11 = 58 - 47 \)
\(12 = \frac{ 7! }{ 84 \cdot 5 }\)
\(13 = 48 - 5 \cdot 7 \)
\(14 = \frac{ \frac{ 7! }{ 45 } }{ 8 }\)
\(15 = \sqrt{58 \cdot 4 - 7 }\)
\(16 = 74 - 58 \)
\(17 = \sqrt{\frac{ 578 }{ \sqrt{4 } }}\)
\(18 = 5^{\frac{ 8 }{ 4 }} - 7 \)
\(19 = \frac{ 57 \cdot 8 }{ 4 ! }\)
\(20 = 4 \cdot 8 - 5 - 7 \)
\(21 = \frac{ 7! }{ 48 \cdot 5 }\)
\(22 = \frac{ 58 }{ \sqrt{4} } - 7 \)
\(23 = \sqrt{784} - 5 \)
\(24 = 78 - 54 \)
\(25 = 57 - 4 \cdot 8 \)
\(26 = \frac{ 78 }{ 5 - \sqrt{4 } }\)
\(27 = 75 - 48 \)
\(28 = \sqrt{57 - 8} \cdot 4 \)
\(29 = 5! - 84 - 7 \)
\(30 = 45 - 7 - 8 \)
\(31 = 4 \cdot 7 - 5 + 8 \)
\(32 = 47 - \frac{ 5! }{ 8 }\)
\(33 = 78 - 45 \)
\(34 = 47 - 5 - 8 \)
\(35 = 4 \cdot 5 + 7 + 8 \)
\(36 = 48 - 5 - 7 \)
\(37 = 5! - ( 87 - 4 )\)
\(38 = 85 - 47 \)
\(39 = 54 - 7 - 8 \)
\(40 = ( 5 + 7 ) \cdot 4 - 8 \)
\(41 = 47 - ( 8 - 5 )!\)
\(42 = 87 - 45 \)
\(43 = 75 - 4 \cdot 8 \)
\(44 = 45 + 7 - 8 \)
\(45 = ( 8 - 7 ) \cdot 45 \)
\(46 = 45 - 7 + 8 \)
\(47 = 58 - 4 - 7 \)
\(48 = \sqrt{48^{7 - 5 }}\)
\(49 = 84 - 5 \cdot 7 \)
\(50 = 47 - 5 + 8 \)
\(51 = 57 + \sqrt{4} - 8 \)
\(52 = 58 - ( 7 - 4 )!\)
\(53 = 54 + 7 - 8 \)
\(54 = ( 8 - 7 ) \cdot 54 \)
\(55 = 54 - 7 + 8 \)
\(56 = ( 5 - 4 ) \cdot 7 \cdot 8 \)
\(57 = 85 - 4 \cdot 7 \)
\(58 = 78 - 4 \cdot 5 \)
\(59 = \frac{ 8 }{ 4 } + 57 \)
\(60 = \sqrt{48 \cdot 75 }\)
\(61 = 57 - 4 + 8 \)
\(62 = \frac{ 5! }{ 8 } + 47 \)
\(63 = 75 - 4 - 8 \)
\(64 = ( 7 - 4 )! + 58 \)
\(65 = 5! - 47 - 8 \)
\(66 = 5! - ( 78 - 4 ! )\)
\(67 = 87 - 4 \cdot 5 \)
\(68 = 74 - ( 8 - 5 )!\)
\(69 = 54 + 7 + 8 \)
\(70 = \sqrt{4}^{7} - 58 \)
\(71 = 74 + 5 - 8 \)
\(72 = 84 - 5 - 7 \)
\(73 = 75 - \frac{ 8 }{ 4 }\)
\(74 = 85 - 4 - 7 \)
\(75 = 58 + 4! - 7 \)
\(76 = 85 - \sqrt{4} - 7 \)
\(77 = 74 - 5 + 8 \)
\(78 = ( 5 - 4 ) \cdot 78 \)
\(79 = 75 - 4 + 8 \)
\(80 = ( 8 - 5 )! + 74 \)
\(81 = 5! - 47 + 8 \)
\(82 = 84 + 5 - 7 \)
\(83 = 5 \cdot 7 + 48 \)
\(84 = \sqrt{84^{7 - 5 }}\)
\(85 = 75 + \sqrt{4} + 8 \)
\(86 = 4 \cdot 7 + 58 \)
\(87 = 5 \cdot 8 + 47 \)
\(88 = 85 - 4 + 7 \)
\(89 = 4 \cdot 8 + 57 \)
\(90 = 85 - \sqrt{4} + 7 \)
\(91 = 75 + 4! - 8 \)
\(92 = 5! - \sqrt{784 }\)
\(93 = ( 4 + 7 ) \cdot 8 + 5 \)
\(94 = 85 + \sqrt{4} + 7 \)
\(95 = ( 4 + 7 + 8 ) \cdot 5 \)
\(96 = ( 7 - 5 ) \cdot 48 \)
\(97 = 78 + 4! - 5 \)
\(98 = 4 \cdot 5 + 78 \)
\(99 = ( 8 - 4 )! + 75 \)
\(100 = \frac{ 7! }{ 48 } - 5 \)