Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Detail) $ in Millions	9 Months Ended
	May 31, 2022 USD ($)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ 1,307.7
Ending balance	1,270.4
Unrealized Gain (Loss) on Derivative Financial Instruments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(7.4)
Other comprehensive gain (loss) before reclassifications	10.7
Amounts reclassified from Accumulated other comprehensive loss	3.8
Ending balance	7.1
Foreign Currency Translation Adjustment
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(35.8)
Other comprehensive gain (loss) before reclassifications	(7.5)
Ending balance	(43.3)
Other
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(0.5)
Other comprehensive gain (loss) before reclassifications	0.1
Ending balance	(0.4)
Accumulated Other Comprehensive (Loss)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(43.7)
Other comprehensive gain (loss) before reclassifications	3.3
Amounts reclassified from Accumulated other comprehensive loss	3.8
Ending balance	$ (36.6)