Leases - Schedule of Other Information Related to Operating Lease (Details) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2022	Nov. 30, 2021	Aug. 31, 2022
Leases [Abstract]
Operating lease cost	$ 8.1	$ 10.5
Variable lease cost	$ 4.2	2.9
Weighted average remaining lease term (in years)	8 years 4 months 24 days		8 years 7 months 6 days
Weighted average discount rate (incremental borrowing rate)	4.40%		4.40%
Lease ROU assets obtained in exchange for lease liabilities	$ 9.7	11.1
Lease ROU assets obtained in exchange for lease liabilities	$ 0.1	$ 1.4