Commitments and Contingencies - Narrative (Details) $ in Millions	12 Months Ended
	Aug. 26, 2023 USD ($) Company Site	Aug. 27, 2022 USD ($)	Aug. 28, 2021 USD ($)
Gain Contingencies [Line Items]
Operating lease, existence of option to extend	true
Operating lease, existence of option to terminate	true
Total rent expense on all leases	$ 18.4	$ 16.7	$ 16.2
Estimated rate of inflation	3.00%
Annual proceeds	$ 0.3
Number of sites related to former operations | Site	2
Balance in escrow account	$ 5.2
Number of insurance companies | Company	3
Outstanding letters of credit	$ 66.5	$ 60.8
Non-cancellable purchase commitments for inventories, software, and services	74.8
Non-cancellable purchase commitments to be paid in less than one year	45.9
Non-cancellable purchase commitments to be paid in one to three year	16.0
Federal | Mexican Tax Authority | Fiscal 2016 Import Taxes
Gain Contingencies [Line Items]
Tax assessment issued	17.0
Tax assessment issued with surcharges, fines and penalties	67.7
Tax assessment issued amount net	$ 84.7
Minimum
Gain Contingencies [Line Items]
Risk-free interest rates utilized	4.30%
Maximum
Gain Contingencies [Line Items]
Risk-free interest rates utilized	4.70%