Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands		12 Months Ended
		Aug. 26, 2023	Aug. 27, 2022	Aug. 28, 2021
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,915,871	$ 1,872,952	$ 1,741,129
Change during the year		529	546	7,134
Balance at end of period		2,003,960	1,915,871	1,872,952
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(24,803)	(17,801)
Change during the year		(1,701)	(7,002)
Balance at end of period		(26,504)	(24,803)	(17,801)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	452	(7,066)
Change during the year	[1]	2,130	7,518
Balance at end of period	[1]	2,582	452	(7,066)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	61	31
Change during the year	[1]	100	30
Balance at end of period	[1]	161	61	31
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(24,290)	(24,836)	(31,970)
Change during the year		529	546
Balance at end of period		$ (23,761)	$ (24,290)	$ (24,836)

[1] Amounts are shown net of tax.