24 math game?

Question

So, for math we're doing the math game 24. For those who don't know, it's a game where you need to use math in order to have 4 numbers reach 24(ex:9x3-2-1). In the standard rules you can only use addition, subtraction, multiplication, and division but if you can find other ways I'll accept those answers as well(ex: (6x4)(1^3)).

So, anyways my teacher asked if we could get all possibilities 1-9 with no repeats, here's the ones I got stuck on:
8 1 6 7
8 2 5 7
9 2 5 6
9 1 4 5
7 3 4 6
9 5 6 7
thanks.

Answer 1

Problems #1 and #5 require something other than the standard operations. The rest can be done...

8167 --> √(8 + 1 + 7) × 6 = 24
8257 --> 8 × (2 × 5 - 7) = 24
9256 --> 9 + 5 × 6 ÷ 2 = 24
9145 --> (9 - 4) × 5 - 1 = 24
7346 --> (√4 × 7 - 6) × 3 = 24
9567 --> (7 - 5) × 9 + 6 = 24

Answer 2

Are you allowed to rearrange the order of the numbers? Or do you have to leave them in the same order they appear and only add operators?

8 1 6 7
-8 + arctan(1) - 6 - 7 or (-8 +45 - 6 -7)

8 2 5 7
8*((2*5)-7)

Answer 3

what functions can you use? Add, subtract, mult, and divide? or is squaring a function you can use? If so... 5^2 - 3 +2 = 24