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Goodwill and Intangible Assets - Narrative (Details) $ in Millions |  | 3 Months Ended | 9 Months Ended
--- | --- | --- | ---
Jun. 01, 2020 USD ($) intangible_asset | May 31, 2020 USD ($) | May 31, 2019 USD ($) | May 31, 2020 USD ($) | May 31, 2019 USD ($)
Goodwill and Intangible Assets Disclosure [Abstract] |  |  |  |  |
Amortization of intangible assets |  | $ 10.8 | $ 7.7 | $ 30.8 | $ 23.1
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract] |  |  |  |  |
Amortization expense in fiscal 2020 |  | 41.5 |  | 41.5 |
Amortization expense in fiscal 2021 |  | 40.1 |  | 40.1 |
Amortization expense in fiscal 2022 |  | 40.0 |  | 40.0 |
Amortization expense in fiscal 2023 |  | 38.9 |  | 38.9 |
Amortization expense in fiscal 2024 |  | $ 38.0 |  | $ 38.0 |
Subsequent Event | Trade Names |  |  |  |  |
Indefinite-lived Intangible Assets [Line Items] |  |  |  |  |
Number of intangible assets | intangible_asset | 13 |  |  |  |
Carrying value of trade names | $ 174.7 |  |  |  |
Impairment charge | $ 1.4 |  |  |  |
Number of impaired intangible assets | intangible_asset | 1 |  |  |  |
Number of intangible assets whose fair values exceeded carrying values | intangible_asset | 12 |  |  |  |
Growth rate | Minimum | Subsequent Event |  |  |  |  |
Indefinite-lived Intangible Assets [Line Items] |  |  |  |  |
Intangible asset measurement input (percent) | 3.00% |  |  |  |
Royalty rates | Minimum | Subsequent Event |  |  |  |  |
Indefinite-lived Intangible Assets [Line Items] |  |  |  |  |
Intangible asset measurement input (percent) | 1.00% |  |  |  |
Royalty rates | Maximum | Subsequent Event |  |  |  |  |
Indefinite-lived Intangible Assets [Line Items] |  |  |  |  |
Intangible asset measurement input (percent) | 4.00% |  |  |  |
Discount rate | Minimum | Subsequent Event |  |  |  |  |
Indefinite-lived Intangible Assets [Line Items] |  |  |  |  |
Intangible asset measurement input (percent) | 10.00% |  |  |  |
Discount rate | Maximum | Subsequent Event |  |  |  |  |
Indefinite-lived Intangible Assets [Line Items] |  |  |  |  |
Intangible asset measurement input (percent) | 13.00% |  |  |  |

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