Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Detail) $ in Millions	3 Months Ended
	Nov. 30, 2021 USD ($)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ 1,307.7
Ending balance	1,237.3
Unrealized Gain (Loss) on Derivative Financial Instruments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(7.4)
Other comprehensive gain (loss) before reclassifications	(3.2)
Amounts reclassified from Accumulated other comprehensive loss	1.0
Ending balance	(9.6)
Foreign Currency Translation Adjustment
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(35.8)
Other comprehensive gain (loss) before reclassifications	(13.9)
Ending balance	(49.7)
Other
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(0.5)
Other comprehensive gain (loss) before reclassifications	(0.1)
Ending balance	(0.6)
Accumulated Other Comprehensive (Loss)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(43.7)
Other comprehensive gain (loss) before reclassifications	(17.2)
Amounts reclassified from Accumulated other comprehensive loss	1.0
Ending balance	$ (59.9)