Stockholders' Equity - Narrative (Details) - USD ($)	3 Months Ended		9 Months Ended
	May 31, 2020	May 31, 2019	May 31, 2020	May 31, 2019	Mar. 24, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]
Repurchase of common stock (in shares)	46,636	175,000	657,136	664,945
Repurchases of common stock	$ 12,410,000	$ 47,555,000	$ 171,005,000	$ 152,139,000
Remaining authorized repurchase amount	$ 287,600,000		287,600,000
Approved addition to authorized amount					$ 220,000,000.0
Cost of shares repurchased from employees			$ 1,600,000	$ 6,200,000
Restricted stock units
Accumulated Other Comprehensive Income (Loss) [Line Items]
Restricted stock vested (in shares)			16,657	75,530,000
Cost of shares repurchased from employees			$ 1,600,000	$ 6,200,000
Treasury Stock
Accumulated Other Comprehensive Income (Loss) [Line Items]
Repurchase of common stock (in shares)	46,636	175,000	657,136	664,945
Repurchases of common stock	$ 12,410,000	$ 47,555,000	$ 171,005,000	$ 152,139,000
Vesting of restricted stock (in shares)	21			27,852
Treasury Stock | Restricted stock units
Accumulated Other Comprehensive Income (Loss) [Line Items]
Vesting of restricted stock (in shares)			6,230