Intangibles and Other Assets, Net - Additional Information (Detail) - USD ($) $ in Millions	12 Months Ended
Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization expense	$ 7.2	$ 8.0	$ 9.3
Future amortization expense, 2025	6.6
Future amortization expense, 2026	6.1
Future amortization expense, 2027	5.2
Future amortization expense, 2028	3.8
Future amortization expense, 2029	$ 2.6
Amortizable intangible assets, weighted-average remaining useful life	6 years 7 months 6 days

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fifth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Remaining amortization period of finite-lived intangible assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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