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.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126954810&loc=d3e3602-108585

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (a)(2)
-URI https://asc.fasb.org/extlink&oid=66006027&loc=d3e16323-109275

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 30
-Section 45
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=6388964&loc=d3e16225-109274

Name:	us-gaap_AmortizationOfIntangibleAssets
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

Intangible Assets - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2023	Feb. 28, 2022	Feb. 28, 2023	Feb. 28, 2022
Finite-Lived Intangible Assets [Line Items]
Weighted average useful life			32 years 9 months 18 days
Amortization expense	$ 21.7	$ 9.1	$ 43.4	$ 19.2
Acquisitions Excluding CGS
Finite-Lived Intangible Assets [Line Items]
Weighted average useful life			9 years 3 months 18 days