Stockholders' Equity - Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	Nov. 30, 2021	Aug. 31, 2021	Nov. 30, 2020	Aug. 31, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	$ 1,098,895	$ 1,016,353	$ 952,573	$ 896,375
Accumulated unrealized losses on cash flow hedges
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	(2,090)	(2,095)
Accumulated foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	(55,580)	(36,867)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	$ (57,670)	$ (38,962)	$ (39,076)	$ (39,293)