Consolidated Statements of Changes in Shareholders' Equity - USD ($) shares in Millions, $ in Millions	Total	Adoption of Accounting Standards Update (ASU) 2020-06	Common Shares	Additional Paid-In Capital	Additional Paid-In Capital Adoption of Accounting Standards Update (ASU) 2020-06	Retained Earnings	Retained Earnings Adoption of Accounting Standards Update (ASU) 2020-06	Accumulated Other Comprehensive Income (Loss)	Treasury Stock
Beginning balance (in shares) at Aug. 28, 2021			51.8
Beginning balance at Aug. 28, 2021	$ 1,056.9		$ 25.9	$ 218.5		$ 1,173.0		$ (0.5)	$ (360.0)
Treasury stock, beginning balance (in shares) at Aug. 28, 2021									(18.7)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	6.9			6.9
Issuance of stock for employee benefit and stock-based awards, net	2.6			(1.9)					$ 4.5
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.2
Issuance of stock for acquisition	22.0			14.7					$ 7.3
Issuance of stock for acquisition (in shares)									0.4
Repurchase of common stock (in shares)									(0.9)
Repurchase of common stock	(64.2)								$ (64.2)
Common stock dividends	(6.1)					(6.1)
Other	0.1					0.1
Net income	190.8					190.8
Ending balance (in shares) at Feb. 26, 2022			51.8
Ending balance at Feb. 26, 2022	1,209.0		$ 25.9	238.2		1,357.8		(0.5)	$ (412.4)
Treasury stock, ending balance (in shares) at Feb. 26, 2022									(19.0)
Beginning balance (in shares) at Aug. 28, 2021			51.8
Beginning balance at Aug. 28, 2021	1,056.9		$ 25.9	218.5		1,173.0		(0.5)	$ (360.0)
Treasury stock, beginning balance (in shares) at Aug. 28, 2021									(18.7)
Ending balance (in shares) at Aug. 27, 2022			51.8
Ending balance at Aug. 27, 2022	$ 1,263.0	$ (33.0)	$ 25.9	256.3	$ (62.0)	1,537.5	$ 29.0	(0.5)	$ (556.2)
Treasury stock, ending balance (in shares) at Aug. 27, 2022	(21.5)								(21.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Accounting standards update, extensible enumeration	Accounting Standards Update 2020-06
Beginning balance (in shares) at Nov. 27, 2021			51.8
Beginning balance at Nov. 27, 2021	$ 1,159.3		$ 25.9	233.8		1,272.7		(0.5)	$ (372.6)
Treasury stock, beginning balance (in shares) at Nov. 27, 2021									(18.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	4.2			4.2
Issuance of stock for employee benefit and stock-based awards, net	0.9			0.2					$ 0.7
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.1
Repurchase of common stock (in shares)									(0.6)
Repurchase of common stock	(40.5)								$ (40.5)
Common stock dividends	(6.1)					(6.1)
Net income	91.2					91.2
Ending balance (in shares) at Feb. 26, 2022			51.8
Ending balance at Feb. 26, 2022	1,209.0		$ 25.9	238.2		1,357.8		(0.5)	$ (412.4)
Treasury stock, ending balance (in shares) at Feb. 26, 2022									(19.0)
Beginning balance (in shares) at Aug. 27, 2022			51.8
Beginning balance at Aug. 27, 2022	$ 1,263.0	$ (33.0)	$ 25.9	256.3	$ (62.0)	1,537.5	$ 29.0	(0.5)	$ (556.2)
Treasury stock, beginning balance (in shares) at Aug. 27, 2022	(21.5)								(21.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	$ 6.5			6.5
Issuance of stock for employee benefit and stock-based awards, net	1.1			(6.9)					$ 8.0
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.4
Repurchase of common stock (in shares)									(0.1)
Repurchase of common stock	(4.9)								$ (4.9)
Common stock dividends	(8.5)					(8.5)
Total comprehensive income	0.1							0.1
Net income	113.0					113.0
Ending balance (in shares) at Feb. 25, 2023			51.8
Ending balance at Feb. 25, 2023	$ 1,337.3		$ 25.9	193.9		1,671.0		(0.4)	$ (553.1)
Treasury stock, ending balance (in shares) at Feb. 25, 2023	(21.2)								(21.2)
Beginning balance (in shares) at Nov. 26, 2022			51.8
Beginning balance at Nov. 26, 2022	$ 1,288.6		$ 25.9	191.2		1,626.7		(0.5)	$ (554.7)
Treasury stock, beginning balance (in shares) at Nov. 26, 2022									(21.3)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	3.5			3.5
Issuance of stock for employee benefit and stock-based awards, net	1.2			(0.8)					$ 2.0
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.1
Repurchase of common stock (in shares)									0.0
Repurchase of common stock	(0.4)								$ (0.4)
Common stock dividends	(8.5)					(8.5)
Total comprehensive income	0.1							0.1
Net income	52.8					52.8
Ending balance (in shares) at Feb. 25, 2023			51.8
Ending balance at Feb. 25, 2023	$ 1,337.3		$ 25.9	$ 193.9		$ 1,671.0		$ (0.4)	$ (553.1)
Treasury stock, ending balance (in shares) at Feb. 25, 2023	(21.2)								(21.2)