Segment Information - Results of Operations (Details) - USD ($) $ in Thousands	3 Months Ended
	Nov. 30, 2022	Nov. 30, 2021	Aug. 31, 2022
Revenues	$ 504,815	$ 424,725
Operating income	171,895	122,661
Capital expenditures	17,960	8,583
Assets	3,977,540		$ 4,014,305
Americas
Revenues	323,367	266,913
Operating income	67,531	55,498
Capital expenditures	15,754	7,203
Assets	3,214,785		3,191,313
EMEA
Revenues	130,738	115,003
Operating income	67,322	40,654
Capital expenditures	573	110
Assets	518,976		580,450
Asia Pacific
Revenues	50,710	42,809
Operating income	37,042	26,509
Capital expenditures	1,633	$ 1,270
Assets	$ 243,779		$ 242,542