Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss, Net of Tax (Detail) $ in Millions	6 Months Ended
	Feb. 28, 2023 USD ($)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ 1,276.9
Ending balance	1,277.3
Unrealized Gain (Loss) on Derivative Financial Instruments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	13.0
Other comprehensive gain before reclassifications	15.0
Amounts reclassified from Accumulated other comprehensive loss	(2.1)
Ending balance	25.9
Foreign Currency Translation Adjustment
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(57.4)
Other comprehensive gain before reclassifications	10.9
Ending balance	(46.5)
Other
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(1.2)
Other comprehensive gain before reclassifications	0.1
Ending balance	(1.1)
Accumulated Other Comprehensive (Loss)
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(45.6)
Other comprehensive gain before reclassifications	26.0
Amounts reclassified from Accumulated other comprehensive loss	(2.1)
Ending balance	$ (21.7)