Acquisitions - Schedule of Acquisition of Business (Details) $ in Thousands	12 Months Ended
Aug. 27, 2022 USD ($) Business	Aug. 28, 2021 USD ($) Business	Aug. 29, 2020 USD ($) Business
Business Acquisition [Line Items]
Goodwill	$ 457,259	$ 429,538	$ 424,844
Aggregate Information Relating to Acquisition of Businesses
Business Acquisition [Line Items]
Number of businesses acquired \| Business	13	8	8
Tangible assets acquired	$ 5,542	$ 812	$ 6,370
Goodwill	27,964	4,533	23,544
Customer contracts	10,450	3,219	12,697
Other intangible assets	807	179	594
Liabilities assumed	0		(1,872)
Acquisition of businesses	$ 44,763	$ 8,743	$ 41,333

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