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Debt - Narrative (Details)
3 Months Ended 9 Months Ended
May 31, 2022
USD ($)
Mar. 01, 2022
USD ($)
May 31, 2022
USD ($)
May 31, 2021
USD ($)
May 31, 2022
USD ($)
May 31, 2021
USD ($)
Aug. 31, 2021
USD ($)
Mar. 05, 2020
Aug. 31, 2019
USD ($)
Mar. 29, 2019
USD ($)
Debt Instrument [Line Items]                    
Borrowed $ 2,125,000,000   $ 2,125,000,000   $ 2,125,000,000          
Repayments of debt         700,000,000 $ 0        
Interest rate swap agreement | Cash flow hedging | Designated as hedging instrument                    
Debt Instrument [Line Items]                    
Fixed rate   1.162%           0.7995%    
Term Loan | 2022 Credit Agreement                    
Debt Instrument [Line Items]                    
Borrowed 875,000,000 $ 1,000,000,000.0 875,000,000   875,000,000   $ 0      
Aggregate principal amount   $ 1,000,000,000.0                
Scheduled amortization payments   1.25%                
Repayments of debt     125,000,000.0              
Senior Notes                    
Debt Instrument [Line Items]                    
Debt issuance costs   $ 9,100,000                
Discount   $ 2,800,000                
Redemption price, percentage   101.00%                
Senior Notes | 2027 Notes                    
Debt Instrument [Line Items]                    
Borrowed 500,000,000   500,000,000   500,000,000   0      
Aggregate principal amount   $ 500,000,000.0                
Stated interest rate   2.90%                
Senior Notes | 2032 Notes                    
Debt Instrument [Line Items]                    
Borrowed $ 500,000,000   500,000,000   500,000,000   $ 0      
Aggregate principal amount   $ 500,000,000.0                
Stated interest rate   3.45%                
Revolving Credit Facility                    
Debt Instrument [Line Items]                    
Interest expense     $ 15,800,000 $ 2,000,000.0 $ 19,600,000 $ 6,000,000.0        
Weighted average interest rate 1.75%   1.75%   1.75%   1.38%      
Revolving Credit Facility | 2019 Revolving Credit Facility                    
Debt Instrument [Line Items]                    
Maximum borrowing capacity                   $ 750,000,000.0
Borrowed                   $ 575,000,000.0
Debt issuance costs                 $ 900,000  
Amortization of remaining debt issuance costs   $ 400,000                
Revolving Credit Facility | 2022 Credit Agreement                    
Debt Instrument [Line Items]                    
Maximum borrowing capacity   500,000,000.0                
Borrowed   250,000,000.0                
Debt issuance costs $ 9,500,000   $ 9,500,000   $ 9,500,000          
Maximum additional borrowings   750,000,000.0                
Commitment fee percentage 12.50%                  
Interest rate during period         1.10%          
Covenants, permitted netting of unrestricted cash and cash equivalents   350,000,000.0                
Covenants, material acquisition aggregate consideration minimum   $ 200,000,000.0                
Covenants, minimum interest coverage ratio   3.00                
Revolving Credit Facility | 2022 Credit Agreement | Minimum                    
Debt Instrument [Line Items]                    
Commitment fee percentage   0.10%                
Covenants, maximum leverage ratio, potential increase   0.50                
Revolving Credit Facility | 2022 Credit Agreement | Maximum                    
Debt Instrument [Line Items]                    
Commitment fee percentage   0.25%                
Covenants, maximum leverage ratio, potential increase   1.00                
Revolving Credit Facility | 2022 Credit Agreement | Beginning with fiscal quarter ending May 31, 2022                    
Debt Instrument [Line Items]                    
Covenants, required maximum leverage ratio   4.00                
Revolving Credit Facility | 2022 Credit Agreement | Beginning with fiscal quarter ending August 31, 2023                    
Debt Instrument [Line Items]                    
Covenants, required maximum leverage ratio   3.75                
Revolving Credit Facility | 2022 Credit Agreement | Beginning with fiscal quarter ending August 31, 2024                    
Debt Instrument [Line Items]                    
Covenants, required maximum leverage ratio   3.50                
Revolving Credit Facility | 2022 Credit Agreement | Secured Overnight Financing Rate (SOFR)                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   0.10%                
Floor interest rate   0                
Revolving Credit Facility | 2022 Credit Agreement | Daily Simple SOFR                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   0.10%                
Floor interest rate   0                
Revolving Credit Facility | 2022 Credit Agreement | Daily Simple SONIA                    
Debt Instrument [Line Items]                    
Floor interest rate   0                
Revolving Credit Facility | 2022 Credit Agreement | EURIBOR                    
Debt Instrument [Line Items]                    
Floor interest rate   0                
Letter of Credit | 2022 Credit Agreement                    
Debt Instrument [Line Items]                    
Maximum borrowing capacity   $ 100,000,000.0                
Swingline Loan | 2022 Credit Agreement                    
Debt Instrument [Line Items]                    
Maximum borrowing capacity   $ 50,000,000.0