Quarterly Financial Data (Unaudited) - Schedule of Quarterly Financial Information (Parenthetical) (Details) - USD ($) $ / shares in Units, $ in Millions		3 Months Ended						12 Months Ended
	Mar. 27, 2018	May 30, 2020	Feb. 29, 2020	Nov. 30, 2019	Aug. 31, 2019	May 25, 2019	Feb. 23, 2019	Aug. 29, 2020	Aug. 31, 2019	Aug. 26, 2017
Quarterly Financial Information Disclosure [Abstract]
Shares repurchased (in shares)		46,667	20,500	50,600	52,650	99,500	45,000	118,000	197,150
Share price (in dollars per share)	$ 124.00	$ 161.65	$ 206.34	$ 197.11	$ 181.61	$ 147.47	$ 139.57	$ 184.67	$ 154.78
Impairment charge of capitalized costs as part of ongoing CRM systems project										$ 55.8
Gain (loss) related to litigation settlement							$ 21.1	$ 21.1
One-time cash payment received for sale of CRM system							13.0	13.0
Hardware received at fair value							$ 0.8	$ 0.8
Diluted earnings per share on settlement agreement of CRM system								$ 0.81