Thanks to vinit for suggesting above optimization.
													
																	Floor sqrt 1 0 8 x 1 2. 
									
	
		
	
																	How do we define the floor of 2 31. 
																	Please write comments if you find anything incorrect or you want to share more information about the topic discussed above. 
																	But 1 is also less than 2 31 and so is 0 and 1 2 3 etc. 
																	The inner one is redundant the outer one of course not. 
															
													
									
	
		
	
																	Well it has to be an integer. 
																	2 is less than 2 31. 
																	For math science nutrition history. 
																	Floor of square root of x cannot be more than x 2 when x 1. 
															
													
									
	
		
	
																	There are lots of integers less than 2 31. 
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																	Choose the greatest one which is 2 in. 
															
													
									
	
		
	
																	So which one do we choose. 
																	The binary search can be further optimized to start with start 0 and end x 2. 
																	And it has to be less than or maybe equal to 2 31 right.