Goodwill and Other Intangible Assets (Narrative) (Details) - USD ($)	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization expense	$ 2,000,000.0	$ 2,200,000	$ 2,500,000
Goodwill impairment	$ 0	$ 0	$ 0