All 100 targets have a solution.
\(1 = 48 - 47 \)
\(2 = \sqrt{\sqrt{784} - 4 !}\)
\(3 = \frac{ \frac{ 84 }{ 4 } }{ 7 }\)
\(4 = \sqrt{784} - 4 !\)
\(5 = \frac{ 48 }{ 4 } - 7 \)
\(6 = ( \frac{ \frac{ 84 }{ 4 } }{ 7 } )!\)
\(7 = \frac{ \sqrt{784} }{ 4 }\)
\(8 = \sqrt{\frac{ 448 }{ 7 }}\)
\(9 = \frac{ 48 }{ 4! } + 7 \)
\(10 = 84 - 74 \)
\(11 = 7 - \sqrt{4 \cdot 4} + 8 \)
\(12 = 7 \cdot 8 - 44 \)
\(13 = \sqrt{44 - 8} + 7 \)
\(14 = \sqrt{\frac{ 784 }{ 4 }}\)
\(15 = \sqrt{484} - 7 \)
\(16 = \frac{ 48 }{ 7 - 4 }\)
\(17 = 8^{\sqrt{4}} - 47 \)
\(18 = 4 \cdot 4! - 78 \)
\(19 = \frac{ 48 }{ 4 } + 7 \)
\(20 = 48 - 4 \cdot 7 \)
\(21 = \sqrt{448 - 7 }\)
\(22 = \frac{ ( 4 + 7 ) \cdot 8 }{ 4 }\)
\(23 = 47 - ( 8 - 4 )!\)
\(24 = \sqrt{784} - 4 \)
\(25 = \frac{ 4^{4} }{ 8 } - 7 \)
\(26 = 74 - 48 \)
\(27 = \frac{ 78 - 4! }{ \sqrt{4 } }\)
\(28 = \frac{ 84 }{ 4 } + 7 \)
\(29 = \sqrt{484} + 7 \)
\(30 = \sqrt{784} + \sqrt{4 }\)
\(31 = 47 - 4! + 8 \)
\(32 = \sqrt{784} + 4 \)
\(33 = \frac{ 74 - 8 }{ \sqrt{4 } }\)
\(34 = 78 - 44 \)
\(35 = 47 - 4 - 8 \)
\(36 = \frac{ 84 }{ 7 } + 4 !\)
\(37 = 84 - 47 \)
\(38 = \frac{ 78 - \sqrt{4} }{ \sqrt{4 } }\)
\(39 = 48 - \sqrt{4} - 7 \)
\(40 = 4 \cdot 7 + 4 + 8 \)
\(41 = 47 + \sqrt{4} - 8 \)
\(42 = 74 - 4 \cdot 8 \)
\(43 = 87 - 44 \)
\(44 = ( 8 - 7 ) \cdot 44 \)
\(45 = 44 - 7 + 8 \)
\(46 = ( 8 - \sqrt{4} ) \cdot 7 + 4 \)
\(47 = \sqrt{47^{\frac{ 8 }{ 4 }}}\)
\(48 = \frac{ 84 \cdot 4 }{ 7 }\)
\(49 = \frac{ 8 }{ 4 } + 47 \)
\(50 = \frac{ 4! }{ 8 } + 47 \)
\(51 = 47 - 4 + 8 \)
\(52 = \sqrt{784} + 4 !\)
\(53 = 47 - \sqrt{4} + 8 \)
\(54 = ( 7 - 4 )! + 48 \)
\(55 = ( 4 + 8 ) \cdot 4 + 7 \)
\(56 = \sqrt{448 \cdot 7 }\)
\(57 = 47 + \sqrt{4} + 8 \)
\(58 = 74 - 4! + 8 \)
\(59 = 44 + 7 + 8 \)
\(60 = 4 \cdot 7 + 4 \cdot 8 \)
\(61 = 87 - 4! - \sqrt{4 }\)
\(62 = 74 - 4 - 8 \)
\(63 = 47 + 4! - 8 \)
\(64 = \frac{ 448 }{ 7 }\)
\(65 = 48 + 4! - 7 \)
\(66 = \sqrt{74^{\sqrt{4}}} - 8 \)
\(67 = 84 - 4! + 7 \)
\(68 = 74 + \sqrt{4} - 8 \)
\(69 = 8^{\sqrt{4}} - \sqrt{4} + 7 \)
\(70 = 74 + 4 - 8 \)
\(71 = 87 - 4 \cdot 4 \)
\(72 = 74 - \frac{ 8 }{ 4 }\)
\(73 = 84 - 4 - 7 \)
\(74 = \sqrt{74^{\frac{ 8 }{ 4 }}}\)
\(75 = 84 - \sqrt{4} - 7 \)
\(76 = 4 \cdot 7 + 48 \)
\(77 = 78 - \frac{ 4 }{ 4 }\)
\(78 = 74 - 4 + 8 \)
\(79 = 4 \cdot 8 + 47 \)
\(80 = \sqrt{4}^{7} - 48 \)
\(81 = 84 + 4 - 7 \)
\(82 = ( 48 - 7 ) \cdot \sqrt{4 }\)
\(83 = 87 - \sqrt{4 \cdot 4 }\)
\(84 = \frac{ 48 }{ 4 } \cdot 7 \)
\(85 = 87 - 4 + \sqrt{4 }\)
\(86 = 74 + 4 + 8 \)
\(87 = 84 - 4 + 7 \)
\(88 = \frac{ 4 }{ 4 } + 87 \)
\(89 = 48 \cdot \sqrt{4} - 7 \)
\(90 = 74 + 4! - 8 \)
\(91 = \sqrt{4 \cdot 4} + 87 \)
\(92 = ( 4 + 7 ) \cdot 8 + 4 \)
\(93 = \frac{ 744 }{ 8 }\)
\(94 = \frac{ 47 \cdot 8 }{ 4 }\)
\(95 = 47 + 48 \)
\(96 = ( 7 - 4 ) \cdot 4 \cdot 8 \)
\(97 = 7^{\sqrt{4}} + 48 \)
\(98 = ( 8 - 4 )! + 74 \)
\(99 = \frac{ 4! }{ \sqrt{4} } + 87 \)
\(100 = 7 \cdot 8 + 44 \)