Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands		12 Months Ended
		Aug. 27, 2022	Aug. 28, 2021	Aug. 29, 2020
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,872,952	$ 1,741,129	$ 1,641,230
Change during the year		546	7,134	1,718
Balance at end of period		1,915,871	1,872,952	1,741,129
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(17,801)	(22,009)
Change during the year		7,002	4,208
Balance at end of period		(24,803)	(17,801)	(22,009)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(7,066)	(10,026)
Change during the year	[1]	7,518	2,960
Balance at end of period	[1]	452	(7,066)	(10,026)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	31	65
Change during the year	[1]	30	(34)
Balance at end of period	[1]	61	31	65
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(24,836)	(31,970)	(33,688)
Change during the year		546	7,134
Balance at end of period		$ (24,290)	$ (24,836)	$ (31,970)

[1] Amounts are shown net of tax.