Stockholders' Equity - Narrative (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Feb. 28, 2022	Feb. 28, 2021	Feb. 28, 2022	Feb. 28, 2021
Class of Stock [Line Items]
Repurchase of common stock (in shares)	0	221,959
Repurchases of common stock	$ 0	$ 71,495	$ 18,639	$ 114,640
Remaining authorized repurchase amount	$ 181,300		$ 181,300
Number of shares repurchased in settlement of employee tax withholding obligations (in shares)			7,422	7,447
Value of shares repurchased in settlement of employee tax withholding obligations			$ 3,300	$ 2,400
Restricted stock units
Class of Stock [Line Items]
Restricted stock vested (in shares)	18,360	18,943
Number of shares repurchased in settlement of employee tax withholding obligations (in shares)	7,162	7,129
Value of shares repurchased in settlement of employee tax withholding obligations	$ 3,100	$ 2,300