Intangible Assets and Goodwill - Schedule of Intangible Assets and Goodwill by Segment (Details) - USD ($) $ in Thousands	May 26, 2023	Aug. 26, 2022
Finite Lived Intangible Assets [Line Items]
Intangible assets, Gross Amount	$ 265,550	$ 138,294
Intangible assets, Accumulated Amortization	(94,135)	(60,482)
Goodwill by segment, Gross Amount	183,089	74,009
Intelligent Platform Solutions
Finite Lived Intangible Assets [Line Items]
Goodwill by segment, Gross Amount	148,771	40,401
Memory Solutions
Finite Lived Intangible Assets [Line Items]
Goodwill by segment, Gross Amount	34,318	33,608
Technology
Finite Lived Intangible Assets [Line Items]
Intangible assets, Gross Amount	151,050	61,594
Intangible assets, Accumulated Amortization	(38,168)	(18,473)
Customer relationships
Finite Lived Intangible Assets [Line Items]
Intangible assets, Gross Amount	85,300	57,500
Intangible assets, Accumulated Amortization	(42,953)	(32,238)
Trademarks/trade names
Finite Lived Intangible Assets [Line Items]
Intangible assets, Gross Amount	29,200	19,200
Intangible assets, Accumulated Amortization	$ (13,014)	$ (9,771)