Equity Plans - Additional Information (Details) - USD ($) shares in Thousands, $ in Millions	3 Months Ended		9 Months Ended
	May 26, 2023	May 27, 2022	May 26, 2023	May 27, 2022
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Ordinary shares, available for issuance (in shares)	7,500		7,500
Unrecognized compensation costs related to awards	$ 1.5		$ 1.5
Unrecognized compensation costs recognition period			1 year 2 months 12 days
Income tax benefits for share-based awards	2.2	$ 5.1	$ 6.2	$ 10.1
Restricted Awards
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Unrecognized compensation costs related to awards	$ 91.9		$ 91.9
Unrecognized compensation costs recognition period			2 years 8 months 12 days
Employee Stock Purchase Plan
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Share issued under purchase plan (in shares)			602	307
Share issued under purchase plan			$ 6.6	$ 6.5