Share-based Compensation - Schedule of Weighted Average Assumptions (Details) - Stock Appreciation Rights (SARs)	12 Months Ended
	Aug. 26, 2023	Aug. 27, 2022	Aug. 28, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Risk-free interest rate	3.97%	1.27%	0.47%
Expected dividend yield	0.62%	0.60%	0.58%
Expected life in years	5 years 5 months 4 days	5 years 2 months 1 day	5 years 8 months 12 days
Expected volatility	29.30%	28.40%	27.50%