Here's some more (without concatenation )
4! / √4 - 4 / 4 = 24 / 2 - 1 = 12 - 1 = 11
4! / √4 + 4/4 = 24/2 + 1 = 12 + 1 = 13
4! / √4 + 4 / √4 = 24/2 + 4/2 = 12 + 2 = 14
4*4 - 4/4 = 16 - 1 = 15
4 + 4 + 4 + 4 = 16
4 * 4 + 4/4 = 16 + 1 = 17
4 * 4 + 4 / √4 = 16 + 4/2 = 16 + 2 = 18
4! - 4 - 4/4 = 24 - 4 - 1 = 19
4!/√4 + 4 + 4 = 24/2 + 4 + 4 = 12 + 4 + 4 = 12 + 8 = 20
4! - 4 + 4/4 = 24 - 4 + 1 = 20 + 1 = 21
4! - 4 + 4/√4 = 24 - 4 + 4/2 = 24 - 4 + 2 = 20 + 2 = 22
4! - (√4 *√4) / 4 = 24 - (2 *2)/4 = 24 - 4/4 = 24 - 1 = 23
4! - 4/√4 + √4 = 24 - 4/2 + 2 = 24 - 2 + 2 = 22 + 2 = 24
