Share-Based Compensation and Employee Benefit Plans - Summary of Options Activity (Details) - 2017 Share Incentive Plan (SGH Plan) $ / shares in Units, shares in Thousands, $ in Thousands	9 Months Ended	12 Months Ended
	May 28, 2021 USD ($) $ / shares shares	Aug. 28, 2020 USD ($) $ / shares shares
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Options outstanding, Shares, Beginning Balance | shares	2,109
Options granted, Shares | shares	250
Options exercised, Shares | shares	(353)
Options cancelled, Shares | shares	(27)
Options outstanding, Shares, Ending Balance | shares	1,979	2,109
Options exercisable, Shares | shares	978
Options outstanding, Weighted average per share exercise price, Beginning Balance | $ / shares	$ 29.45
Options granted, Weighted average per share exercise price | $ / shares	26.99
Options exercised, Weighted average per share exercise price | $ / shares	27.03
Options cancelled, Weighted average per share exercise price | $ / shares	32.09
Options outstanding, Weighted average per share exercise price, Ending Balance | $ / shares	29.53	$ 29.45
Options exercisable, Weighted average per share exercise price | $ / shares	$ 28.76
Options outstanding, Weighted average remaining contractual term (years)	6 years 7 months 6 days	6 years 11 months 12 days
Options exercisable, Weighted average remaining contractual term (years)	5 years 11 months 1 day
Options outstanding, Aggregate intrinsic value | $	$ 35,352	$ 7,225
Options exercisable, Aggregate intrinsic value | $	$ 18,235