Leases - Components of Operating Lease Costs (Detail) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2022	May 31, 2021
Leases [Abstract]
Operating lease expense	$ 2.7	$ 2.9	$ 7.9	$ 10.4
Short-term lease expense	1.1	1.0	3.8	3.6
Total	$ 3.8	$ 3.9	$ 11.7	$ 14.0