Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Detail) $ in Millions	6 Months Ended
	Feb. 29, 2024 USD ($)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ 1,254.6
Ending balance	1,299.9
Unrealized Gain (Loss) on Derivative Financial Instruments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	27.0
Other comprehensive gain before reclassifications	7.1
Amounts reclassified from Accumulated other comprehensive loss	(7.5)
Ending balance	26.6
Foreign Currency Translation Adjustment
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(32.1)
Other comprehensive gain before reclassifications	(1.8)
Ending balance	(33.9)
Other
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(2.2)
Other comprehensive gain before reclassifications	0.6
Ending balance	(1.6)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(7.3)
Other comprehensive gain before reclassifications	5.9
Amounts reclassified from Accumulated other comprehensive loss	(7.5)
Ending balance	$ (8.9)