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. 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)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	8.2			8.2
Issuance of stock for employee benefit and stock-based awards, net	1.0			(7.0)					$ 8.0
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.4
Repurchase of common stock	(24.9)								$ (24.9)
Repurchase of common stock (in shares)									(0.5)
Common stock dividends	(25.2)					(25.2)
Other comprehensive income	0.1							0.1
Net income	172.1					172.1
Ending balance (in shares) at May. 27, 2023			51.8
Ending balance at May. 27, 2023	1,361.3		$ 25.9	195.5		1,713.4		(0.4)	$ (573.1)
Treasury stock, ending balance (in shares) at May. 27, 2023									(21.6)
Beginning balance (in shares) at Feb. 25, 2023			51.8
Beginning balance at Feb. 25, 2023	1,337.3		$ 25.9	193.9		1,671.0		(0.4)	$ (553.1)
Treasury stock, beginning balance (in shares) at Feb. 25, 2023									(21.2)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	1.7			1.7
Issuance of stock for employee benefit and stock-based awards, net	(0.1)			(0.1)
Repurchase of common stock	(20.0)								$ (20.0)
Repurchase of common stock (in shares)									(0.4)
Common stock dividends	(16.7)					(16.7)
Net income	59.1					59.1
Ending balance (in shares) at May. 27, 2023			51.8
Ending balance at May. 27, 2023	1,361.3		$ 25.9	195.5		1,713.4		(0.4)	$ (573.1)
Treasury stock, ending balance (in shares) at May. 27, 2023									(21.6)
Beginning balance (in shares) at Aug. 26, 2023			51.8
Beginning balance at Aug. 26, 2023	$ 1,368.1		$ 25.9	197.7		1,747.8		(0.4)	$ (602.9)
Treasury stock, beginning balance (in shares) at Aug. 26, 2023	(22.0)								(22.0)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Partial repurchase of convertible notes	$ (22.2)			(22.2)
Partial unwind of convertible note bond hedge	55.8			55.8
Partial unwind of convertible note warrant	(25.3)			(25.3)
Convertible note bond hedge purchase, net of tax	(51.9)			(51.9)
Issuance of convertible note warrant	31.3			31.3
Stock-based compensation	11.5			11.5
Issuance of stock for employee benefit and stock-based awards, net	1.4			(5.3)					$ 6.7
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.2
Repurchase of common stock	(64.8)			(0.5)					$ (64.3)
Repurchase of common stock (in shares)									(1.0)
Common stock dividends	(27.6)					(27.6)
Net income	42.1					42.1
Ending balance (in shares) at May. 25, 2024			51.8
Ending balance at May. 25, 2024	$ 1,318.4		$ 25.9	191.1		1,762.3		(0.4)	$ (660.5)
Treasury stock, ending balance (in shares) at May. 25, 2024	(22.8)								(22.8)
Beginning balance (in shares) at Feb. 24, 2024			51.8
Beginning balance at Feb. 24, 2024	$ 1,324.6		$ 25.9	188.1		1,751.6		(0.4)	$ (640.6)
Treasury stock, beginning balance (in shares) at Feb. 24, 2024									(22.5)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	3.4			3.4
Issuance of stock for employee benefit and stock-based awards, net	0.0			(0.2)					$ 0.2
Repurchase of common stock	(20.3)			(0.2)					$ (20.1)
Repurchase of common stock (in shares)									(0.3)
Common stock dividends	(18.3)					(18.3)
Net income	29.0					29.0
Ending balance (in shares) at May. 25, 2024			51.8
Ending balance at May. 25, 2024	$ 1,318.4		$ 25.9	$ 191.1		$ 1,762.3		$ (0.4)	$ (660.5)
Treasury stock, ending balance (in shares) at May. 25, 2024	(22.8)								(22.8)