Basis of Presentation (Details) - USD ($) shares in Millions, $ in Millions	3 Months Ended		6 Months Ended
	Feb. 25, 2023	Feb. 26, 2022	Feb. 25, 2023	Feb. 26, 2022	Nov. 26, 2022	Aug. 27, 2022
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Decrease in additional paid-in capital	$ (193.9)		$ (193.9)			$ (256.3)
Long-term debt, net	591.0		591.0			545.9
Decrease in deferred income tax liability	0.0		0.0			(6.1)
Increase in retained earnings	$ 1,671.0		1,671.0			$ 1,537.5
Reduction of non-cash interest expense		$ (3.7)	$ 0.0	$ (7.3)
Dilutive impact of convertible notes (in shares)	4.7	0.4	4.7	0.5
Accounting Standards Update 2020-06
New Accounting Pronouncements or Change in Accounting Principle [Line Items]
Decrease in additional paid-in capital					$ 62.0
Long-term debt, net					43.8
Decrease in deferred income tax liability					10.8
Increase in retained earnings					$ 29.0
Reduction of non-cash interest expense	$ 3.7		$ 7.3
Dilutive impact of convertible notes (in shares)			4.7