Goodwill and Intangible Assets - Narrative (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
May 31, 2025	May 31, 2024	May 31, 2025	May 31, 2024
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization of intangible assets	$ 20.0	$ 10.0	$ 45.5	$ 29.9

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.

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