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Acquisitions - Schedule of Acquisition of Business (Details) $ in Thousands | 12 Months Ended
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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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