All 100 targets have a solution.
\(1 = \frac{ \sqrt{87 - 6} }{ 9 }\)
\(2 = \sqrt{76 - 8 \cdot 9 }\)
\(3 = \sqrt{78 - 69 }\)
\(4 = 76 - 8 \cdot 9 \)
\(5 = 8 \cdot 9 - 67 \)
\(6 = \sqrt{78 - 69 }!\)
\(7 = 86 - 79 \)
\(8 = \frac{ 78 - 6 }{ 9 }\)
\(9 = 78 - 69 \)
\(10 = \frac{ 78 }{ 6 } - \sqrt{9 }\)
\(11 = 79 - 68 \)
\(12 = 6 + 7 + 8 - 9 \)
\(13 = 89 - 76 \)
\(14 = \frac{ 87 - \sqrt{9} }{ 6 }\)
\(15 = \frac{ 87 + \sqrt{9} }{ 6 }\)
\(16 = \sqrt{\frac{ 768 }{ \sqrt{9 } }}\)
\(17 = \sqrt{\frac{ 867 }{ \sqrt{9 } }}\)
\(18 = 87 - 69 \)
\(19 = \frac{ 96 }{ 8 } + 7 \)
\(20 = \frac{ 98 }{ 7 } + 6 \)
\(21 = \sqrt{\sqrt{7^{6}} + 98 }\)
\(22 = 89 - 67 \)
\(23 = 86 - 7 \cdot 9 \)
\(24 = 78 - 6 \cdot 9 \)
\(25 = \frac{ 67 + 8 }{ \sqrt{9 } }\)
\(26 = \frac{ 78 }{ 9 - 6 }\)
\(27 = \frac{ 87 - 6 }{ \sqrt{9 } }\)
\(28 = \frac{ 76 + 8 }{ \sqrt{9 } }\)
\(29 = 97 - 68 \)
\(30 = 6 + 7 + 8 + 9 \)
\(31 = 98 - 67 \)
\(32 = \frac{ 78 }{ \sqrt{9} } + 6 \)
\(33 = 87 - 6 \cdot 9 \)
\(34 = \frac{ 68 }{ 9 - 7 }\)
\(35 = \frac{ 87 }{ \sqrt{9} } + 6 \)
\(36 = 6^{\frac{ 7 + 9 }{ 8 }}\)
\(37 = 6 \cdot 7 - 8 + \sqrt{9 }\)
\(38 = \frac{ 76 }{ 8 - \sqrt{9 }! }\)
\(39 = \frac{ 78 }{ 6 } \cdot \sqrt{9 }\)
\(40 = 96 - 7 \cdot 8 \)
\(41 = 6 \cdot 7 + 8 - 9 \)
\(42 = \sqrt{9}!! - 678 \)
\(43 = \frac{ 86 }{ 9 - 7 }\)
\(44 = 6^{9 - 7} + 8 \)
\(45 = ( 6 + 7 - 8 ) \cdot 9 \)
\(46 = 6 \cdot 8 + 7 - 9 \)
\(47 = 89 - 6 \cdot 7 \)
\(48 = \sqrt{768 \cdot \sqrt{9 }}\)
\(49 = 97 - 6 \cdot 8 \)
\(50 = 67 - 8 - 9 \)
\(51 = \sqrt{867 \cdot \sqrt{9 }}\)
\(52 = 68 - 7 - 9 \)
\(53 = 7 \cdot 8 + 6 - 9 \)
\(54 = 69 - 7 - 8 \)
\(55 = 6 \cdot 9 - 7 + 8 \)
\(56 = 98 - 6 \cdot 7 \)
\(57 = \frac{ 76 \cdot \sqrt{9}! }{ 8 }\)
\(58 = \frac{ 87 \cdot 6 }{ 9 }\)
\(59 = 76 - 8 - 9 \)
\(60 = 78 - 6 \cdot \sqrt{9 }\)
\(61 = 7 \cdot 9 + 6 - 8 \)
\(62 = 67 - 8 + \sqrt{9 }\)
\(63 = 78 - 6 - 9 \)
\(64 = 68 - 7 + \sqrt{9 }\)
\(65 = 79 - 6 - 8 \)
\(66 = 67 + 8 - 9 \)
\(67 = ( 9 - 8 ) \cdot 67 \)
\(68 = 67 - 8 + 9 \)
\(69 = 789 - 6 !\)
\(70 = 68 - 7 + 9 \)
\(71 = 76 - 8 + \sqrt{9 }\)
\(72 = 87 - 6 - 9 \)
\(73 = 8 \cdot 9 - 6 + 7 \)
\(74 = 9^{8 - 6} - 7 \)
\(75 = 76 + 8 - 9 \)
\(76 = ( 9 - 8 ) \cdot 76 \)
\(77 = 76 - 8 + 9 \)
\(78 = 798 - 6 !\)
\(79 = \sqrt{79^{8 - 6 }}\)
\(80 = \frac{ 6 }{ \sqrt{9} } + 78 \)
\(81 = 78 - 6 + 9 \)
\(82 = 86 - 7 + \sqrt{9 }\)
\(83 = 97 - 6 - 8 \)
\(84 = 67 + 8 + 9 \)
\(85 = 98 - 6 - 7 \)
\(86 = \sqrt{86^{9 - 7 }}\)
\(87 = 76 + 8 + \sqrt{9 }\)
\(88 = 86 - 7 + 9 \)
\(89 = ( 7 - 6 ) \cdot 89 \)
\(90 = 87 - 6 + 9 \)
\(91 = 8 \cdot \sqrt{9} + 67 \)
\(92 = ( 7 - \sqrt{9} )! + 68 \)
\(93 = 76 + 8 + 9 \)
\(94 = \frac{ 6! }{ 8 } + 7 - \sqrt{9 }\)
\(95 = 96 + 7 - 8 \)
\(96 = ( 8 - 7 ) \cdot 96 \)
\(97 = 96 - 7 + 8 \)
\(98 = ( 7 - 6 ) \cdot 98 \)
\(99 = 97 - 6 + 8 \)
\(100 = 8 \cdot \sqrt{9} + 76 \)