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Investments and Fair Value Measurements - Assets and Liabilities Measured at Fair Value (Details) - USD ($)	3 Months Ended
	Nov. 26, 2022	Nov. 27, 2021	Aug. 27, 2022
Fair Value, Measurements, Recurring
Assets that fund deferred compensation
Domestic equity funds	$ 1,700,000		$ 1,200,000
International equity funds	100,000		100,000
Fixed income funds	200,000		100,000
Total assets at fair value	2,000,000.0		1,400,000
Contingent consideration
Earnout liability	40,200,000		39,800,000
Total liabilities at fair value	40,200,000		39,800,000
Fair Value, Measurements, Recurring | Level 1
Assets that fund deferred compensation
Domestic equity funds	1,700,000		1,200,000
International equity funds	100,000		100,000
Fixed income funds	200,000		100,000
Total assets at fair value	2,000,000.0		1,400,000
Contingent consideration
Earnout liability	0		0
Total liabilities at fair value	0		0
Fair Value, Measurements, Recurring | Level 2
Assets that fund deferred compensation
Domestic equity funds	0		0
International equity funds	0		0
Fixed income funds	0		0
Total assets at fair value	0		0
Contingent consideration
Earnout liability	0		0
Total liabilities at fair value	0		0
Fair Value, Measurements, Recurring | Level 3
Assets that fund deferred compensation
Domestic equity funds	0		0
International equity funds	0		0
Fixed income funds	0		0
Total assets at fair value	0		0
Contingent consideration
Earnout liability	40,200,000		39,800,000
Total liabilities at fair value	40,200,000		$ 39,800,000
Fair Value, Nonrecurring
Contingent consideration
Asset impairment charges	$ 0	$ 0

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Amount of write-down of assets recognized in the income statement. Includes, but is not limited to, losses from tangible assets, intangible assets and goodwill.

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