Let's see what we have here 
```'Demon Guard Flageon: Who dares to disturb my slumber?...A human?what is your name human?
You: yes
Demon Guard Flageon: Listen close, yes.	To pass through you must give me a key of certain shape and size.	I do not expect mere mortals to pass this test and win the Flag of Life.	So here is a hint: the shape of the key is a square.	But I will not tell you the size.	You have 3 tries!
	| How lucky! Look in your backpack. You have a square-key-making device.	| huh... weird thing to carry around if you ask me.	| Anyways.	| The problem is the device needs the edge length as input to make the key...
Input edge length: 1
*mechanical whirring*...*pop*
Demon Guard Flageon: The size of your key is off by 1 sq cm.	You have 2 more attempts left
Input edge length: 5
*mechanical whirring*...*pop*
Demon Guard Flageon: The size of your key is off by 25 sq cm.	You have 1 more attempts left
Input edge length: 9
*mechanical whirring*...*pop*
Demon Guard Flageon: The size of your key is off by 81 sq cm.	You have 0 more attempts left
```
Seems like we need to reach the size of 0 somehow, let's see what we are able to do 
```'Demon Guard Flageon: Who dares to disturb my slumber?...A human?what is your name human?
You: kokos
Demon Guard Flageon: Listen close, kokos.	To pass through you must give me a key of certain shape and size.	I do not expect mere mortals to pass this test and win the Flag of Life.	So here is a hint: the shape of the key is a square.	But I will not tell you the size.	You have 3 tries!
	| How lucky! Look in your backpack. You have a square-key-making device.	| huh... weird thing to carry around if you ask me.	| Anyways.	| The problem is the device needs the edge length as input to make the key...
Input edge length: 0
	| Device only takes positive integers as input |
Input edge length: -1
	| Device only takes positive integers as input |
Input edge length: 50000
*mechanical whirring*...*pop*
Demon Guard Flageon: The size of your key is off by -1794967296 sq cm.	You have 0 more attempts left
```
Whoopa seems like we have an 32bit integer overflow here. Knowing that sqrt(4294967295) ~= 65536, we should have everything needed to solve this challenge. 
```'Demon Guard Flageon: Who dares to disturb my slumber?...A human?what is your name human?
You: kokos
Demon Guard Flageon: Listen close, kokos.	To pass through you must give me a key of certain shape and size.	I do not expect mere mortals to pass this test and win the Flag of Life.	So here is a hint: the shape of the key is a square.	But I will not tell you the size.	You have 3 tries!
	| How lucky! Look in your backpack. You have a square-key-making device.	| huh... weird thing to carry around if you ask me.	| Anyways.	| The problem is the device needs the edge length as input to make the key...
Input edge length: 65536
*mechanical whirring*...*pop*
Demon Guard Flageon: Congratulation! You have completed this task.	The Flag of Life is now your's
		===============================================		| darkCTF{-2147483648_c0m3s_aft3r_2147483647} |		===============================================```
Nice :)