All 100 targets have a solution.
\(1 = 47^{8 - 8 }\)
\(2 = \sqrt{\frac{ 84 }{ 7 } - 8 }\)
\(3 = 87 - 84 \)
\(4 = \frac{ 84 }{ 7 } - 8 \)
\(5 = \sqrt{88 - 7} - 4 \)
\(6 = 84 - 78 \)
\(7 = \sqrt{48 - 7 + 8 }\)
\(8 = \frac{ 48 + 8 }{ 7 }\)
\(9 = ( 8 - 7 )^{4} + 8 \)
\(10 = 74 - 8 \cdot 8 \)
\(11 = 4 + 7 - 8 + 8 \)
\(12 = \frac{ 88 - 4 }{ 7 }\)
\(13 = \frac{ 48 }{ 8 } + 7 \)
\(14 = 88 - 74 \)
\(15 = \frac{ 88 }{ 4 } - 7 \)
\(16 = \frac{ 88 + 4! }{ 7 }\)
\(17 = 8 \cdot 8 - 47 \)
\(18 = \sqrt{( 88 - 7 ) \cdot 4 }\)
\(19 = 7 - 4 + 8 + 8 \)
\(20 = \sqrt{784} - 8 \)
\(21 = ( 4 - \frac{ 8 }{ 8 } ) \cdot 7 \)
\(22 = \frac{ 8 }{ 4 } \cdot 7 + 8 \)
\(23 = 87 - 8^{\sqrt{4 }}\)
\(24 = ( \frac{ 84 }{ 7 } - 8 )!\)
\(25 = ( 8 - 4 ) \cdot 8 - 7 \)
\(26 = \frac{ 78 \cdot 8 }{ 4 ! }\)
\(27 = 4 + 7 + 8 + 8 \)
\(28 = \sqrt{788 - 4 }\)
\(29 = \sqrt{848 - 7 }\)
\(30 = 78 - 48 \)
\(31 = 47 - 8 - 8 \)
\(32 = ( 8 - 7 ) \cdot 4 \cdot 8 \)
\(33 = 48 - 7 - 8 \)
\(34 = ( 8 - \sqrt{4} ) \cdot 7 - 8 \)
\(35 = \frac{ 78 - 8 }{ \sqrt{4 } }\)
\(36 = \sqrt{784} + 8 \)
\(37 = \frac{ 88 }{ \sqrt{4} } - 7 \)
\(38 = ( 7 + 8 ) \cdot \sqrt{4} + 8 \)
\(39 = 87 - 48 \)
\(40 = \sqrt{4}^{7} - 88 \)
\(41 = 88 - 47 \)
\(42 = \frac{ 48 \cdot 7 }{ 8 }\)
\(43 = 47 - \sqrt{8 + 8 }\)
\(44 = 4 \cdot 7 + 8 + 8 \)
\(45 = 47 - \sqrt{\sqrt{8 + 8 }}\)
\(46 = 47 - \frac{ 8 }{ 8 }\)
\(47 = 47 - 8 + 8 \)
\(48 = \frac{ 8 }{ 8 } + 47 \)
\(49 = 48 - 7 + 8 \)
\(50 = 74 - \sqrt{8 + 8 }!\)
\(51 = \sqrt{8 + 8} + 47 \)
\(52 = \frac{ 7! }{ 84 } - 8 \)
\(53 = 8 \cdot 8 - 4 - 7 \)
\(54 = 78 - ( 8 - 4 )!\)
\(55 = 87 - 4 \cdot 8 \)
\(56 = \frac{ 8! }{ 7! } + 48 \)
\(57 = 88 - 4! - 7 \)
\(58 = 74 - 8 - 8 \)
\(59 = 8 \cdot 8 + \sqrt{4} - 7 \)
\(60 = 88 - 4 \cdot 7 \)
\(61 = 8 \cdot 8 + 4 - 7 \)
\(62 = 78 - 4! + 8 \)
\(63 = 47 + 8 + 8 \)
\(64 = \frac{ 8^{7 - 4} }{ 8 }\)
\(65 = 7^{\sqrt{4}} + 8 + 8 \)
\(66 = 78 - 4 - 8 \)
\(67 = 8 \cdot 8 - 4 + 7 \)
\(68 = 78 - \sqrt{4} - 8 \)
\(69 = 84 - 7 - 8 \)
\(70 = 74 - \sqrt{8 + 8 }\)
\(71 = 87 - 4! + 8 \)
\(72 = 78 + \sqrt{4} - 8 \)
\(73 = 74 - \frac{ 8 }{ 8 }\)
\(74 = 74 - 8 + 8 \)
\(75 = \frac{ 8 }{ 8 } + 74 \)
\(76 = 78 - \frac{ 8 }{ 4 }\)
\(77 = 88 - 4 - 7 \)
\(78 = \sqrt{8 + 8} + 74 \)
\(79 = 88 - \sqrt{4} - 7 \)
\(80 = \frac{ 8 }{ 4 } + 78 \)
\(81 = \frac{ 4! }{ 8 } + 78 \)
\(82 = 78 - 4 + 8 \)
\(83 = 84 + 7 - 8 \)
\(84 = ( 8 - 7 ) \cdot 84 \)
\(85 = 84 - 7 + 8 \)
\(86 = \sqrt{78^{\sqrt{4}}} + 8 \)
\(87 = \sqrt{87^{\frac{ 8 }{ 4 }}}\)
\(88 = 78 + \sqrt{4} + 8 \)
\(89 = \frac{ 8 }{ 4 } + 87 \)
\(90 = 74 + 8 + 8 \)
\(91 = 87 - 4 + 8 \)
\(92 = ( 4 + 8 ) \cdot 7 + 8 \)
\(93 = 87 - \sqrt{4} + 8 \)
\(94 = 78 + 4! - 8 \)
\(95 = \sqrt{87^{\sqrt{4}}} + 8 \)
\(96 = \frac{ 84 }{ 7 } \cdot 8 \)
\(97 = \frac{ 7! }{ 48 } - 8 \)
\(98 = \frac{ 784 }{ 8 }\)
\(99 = 84 + 7 + 8 \)
\(100 = \sqrt{\sqrt{( \frac{ 4! }{ 8 } + 7 )^{8 }}}\)