Leases - Schedule of Other Information Related to Operating Lease (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021	Aug. 31, 2021
Leases [Abstract]
Operating lease cost	$ 9,800	$ 10,700	$ 30,500	$ 32,200
Variable lease cost	$ 3,200	$ 2,600	$ 8,900	10,300
Weighted average remaining lease term (in years)	8 years 8 months 12 days		8 years 8 months 12 days		9 years 4 months 24 days
Weighted average discount rate (incremental borrowing rate)	4.30%		4.30%		4.30%
Cash paid for amounts included in the measurement of lease liabilities			$ 32,900	30,900
Lease ROU assets obtained in exchange for lease liabilities			9,300	5,500
Reductions to ROU assets resulting from reductions to lease liabilities			$ (11,700)	$ 0