Leases - Components of Operating Lease Costs (Detail) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	May 31, 2024	May 31, 2023	May 31, 2024	May 31, 2023
Leases [Abstract]
Operating lease expense	$ 4.1	$ 2.9	$ 12.9	$ 9.3
Short-term lease expense	2.0	2.9	4.7	7.3
Total	$ 6.1	$ 5.8	$ 17.6	$ 16.6