Segment Information - Results of Operations and Assets (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2023	Feb. 28, 2022	Feb. 28, 2023	Feb. 28, 2022	Aug. 31, 2022
Revenues	$ 515,085	$ 431,119	$ 1,019,900	$ 855,844
Operating income	169,250	123,348	341,145	246,009
Capital expenditures	17,456	11,963	35,416	20,546
Asset impairments	447	10,292	729	13,987
Assets	4,001,075		4,001,075		$ 4,014,305
Americas
Revenues	331,121	273,659	654,488	540,572
Operating income	61,181	48,903	128,712	104,401
Capital expenditures	15,589	10,346	31,343	17,549
Asset impairments		10,200		13,900
Assets	3,189,973		3,189,973		3,191,313
EMEA
Revenues	132,508	114,591	263,246	229,594
Operating income	68,941	45,944	136,263	86,598
Capital expenditures	739	252	1,312	362
Assets	561,294		561,294		580,450
Asia Pacific
Revenues	51,456	42,869	102,166	85,678
Operating income	39,128	28,501	76,170	55,010
Capital expenditures	1,128	$ 1,365	2,761	$ 2,635
Assets	$ 249,808		$ 249,808		$ 242,542