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Basis of Presentation (Details) - USD ($)
shares in Millions, $ in Millions
 3 Months Ended
Nov. 26, 2022
Nov. 27, 2021
Aug. 27, 2022
Accounting Policies [Abstract]      
Deferred FICA liability $ 8.1    
Refundable tax credit, outstanding 0.8    
New Accounting Pronouncements or Change in Accounting Principle [Line Items]      
Decrease in additional paid-in capital (191.2)   $ (256.3)
Long-term debt, net 590.4   545.9
Decrease in deferred income tax liability 0.0   (6.1)
Increase in retained earnings 1,626.7   $ 1,537.5
Reduction of non-cash interest expense $ 0.0 $ (3.6)  
Dilutive impact of convertible notes (in shares) 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 $ 3.6    
Dilutive impact of convertible notes (in shares) 4.7