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. 29, 2020			51.8
Beginning balance at Aug. 29, 2020	$ 827.5		$ 25.9	$ 203.8		$ 913.6		$ (0.5)	$ (315.3)
Treasury stock, beginning balance (in shares) at Aug. 29, 2020									(18.1)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	15.3			15.3
Issuance of stock for employee benefit and stock-based awards, net	2.3			(0.6)					$ 2.9
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.2
Issuance of stock for settlement of earnout liability	0.0
Repurchase of common stock	(47.6)								$ (47.6)
Repurchase of common stock (in shares)									(0.8)
Common stock dividends declared	(22.5)					(22.5)
Net income	281.9					281.9
Ending balance (in shares) at Aug. 28, 2021			51.8
Ending balance at Aug. 28, 2021	1,056.9		$ 25.9	218.5		1,173.0		(0.5)	$ (360.0)
Treasury stock, ending balance (in shares) at Aug. 28, 2021									(18.7)
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Stock-based compensation	17.1			17.1
Issuance of stock for employee benefit and stock-based awards, net	2.9			(2.5)					$ 5.4
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
Issuance of stock for settlement of earnout liability	13.2			7.8					$ 5.4
Issuance of stock for settlement of earnout liability (in shares)									0.2
Repurchase of common stock	(214.3)								$ (214.3)
Repurchase of common stock (in shares)									(3.6)
Common stock dividends declared	(26.2)					(26.2)
Other	0.8			0.7		0.1
Net income	390.6					390.6
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
Stock-based compensation	$ 10.9			10.9
Issuance of stock for employee benefit and stock-based awards, net	1.2			(7.2)					$ 8.4
Issuance of stock for employee benefit and stock-based awards, net (in shares)									0.4
Issuance of stock for settlement of earnout liability	0.0
Repurchase of common stock	(55.4)			(0.3)					$ (55.1)
Repurchase of common stock (in shares)									(0.9)
Common stock dividends declared	(34.6)					(34.6)
Other comprehensive income	0.1							0.1
Net income	215.9					215.9
Ending balance (in shares) at Aug. 26, 2023			51.8
Ending balance at Aug. 26, 2023	$ 1,368.1		$ 25.9	$ 197.7		$ 1,747.8		$ (0.4)	$ (602.9)
Treasury stock, ending balance (in shares) at Aug. 26, 2023	(22.0)								(22.0)