Investments and Fair Value Measurements - Fair Value of Contingent Consideration (Details) - USD ($) $ in Millions	3 Months Ended	6 Months Ended
Feb. 25, 2023	Feb. 26, 2022	Feb. 25, 2023	Feb. 26, 2022
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Beginning fair value - contingent consideration	$ 40.2	$ 30.6	$ 39.8	$ 0.0
Additions	0.0	0.0	0.0	24.2
Fair value adjustments	1.6	6.5	2.0	12.9
Ending fair value - contingent consideration	$ 41.8	$ 37.1	$ 41.8	$ 37.1

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

No definition available.

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- Definition

Amount of gain (loss) recognized in income from liability measured at fair value on recurring basis using unobservable input (level 3).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

+ Details

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- Definition

Amount of purchases of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

+ Details

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- Definition

Fair value of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=126976982&loc=d3e19207-110258

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