Accumulated Other Comprehensive Loss - Components of Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands		12 Months Ended
		Aug. 29, 2020	Aug. 31, 2019	Aug. 25, 2018
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		$ 1,641,230	$ 1,464,967	$ 1,453,192
Change during the year		1,718	(8,529)	(3,641)
Balance at end of period		1,741,129	1,641,230	1,464,967
Foreign Currency Translation
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(24,640)	(21,116)
Change during the year		2,631	(3,524)
Balance at end of period		(22,009)	(24,640)	(21,116)
Pension-related
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	(9,239)	(4,135)
Change during the year	[1]	(787)	(5,104)
Balance at end of period	[1]	(10,026)	(9,239)	(4,135)
Derivative Financial Instruments
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period	[1]	191	92
Change during the year	[1]	(126)	99
Balance at end of period	[1]	65	191	92
Accumulated Other Comprehensive Loss
AOCI Attributable to Parent, Net of Tax [Roll Forward]
Balance at beginning of period		(33,688)	(25,159)	(21,518)
Change during the year		1,718	(8,529)
Balance at end of period		$ (31,970)	$ (33,688)	$ (25,159)

[1] Amounts are shown net of tax.