Employee Benefit Plans - Narrative (Details) $ in Millions	3 Months Ended	9 Months Ended
May 25, 2024 USD ($) RetirementPlan	May 27, 2023 USD ($)	May 25, 2024 USD ($) RetirementPlan	May 27, 2023 USD ($)	Aug. 26, 2023 USD ($)
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Contributions charged to expense under the plan	$ 5.1	$ 4.4	$ 15.2	$ 14.3
SERP
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Number of frozen non-contributory defined benefit pension plans \| RetirementPlan	1		1
Amounts charged to expense related to the plans	$ 0.4	0.4	$ 1.3	1.3
Non-qualified Deferred Compensation Plan
Defined Benefit Plans and Other Postretirement Benefit Plans Table Text Block [Line Items]
Amounts charged to expense related to the plans	0.2	$ 0.1	0.6	$ 0.3
NQDC Plan assets	3.1		3.1		$ 2.0
NQDC Plan liabilities	$ 1.3		$ 1.3		$ 0.5

Defined Benefit Plan, Number Of Frozen Plans

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Aggregate carrying value as of the balance sheet date of the liabilities for all deferred compensation arrangements. Represents currently earned compensation under compensation arrangements that is not actually paid until a later date.

+ References

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Carrying amount as of the balance sheet date of assets held under deferred compensation agreements.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(17))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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Amount of cost for defined contribution plan.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 715
-SubTopic 70
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480794/715-70-50-1

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Amount of cost (reversal of cost) for pension benefits. Excludes other postretirement benefits.

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