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Intangibles and Other Assets, Net - Additional Information (Detail) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
May 31, 2021
May 31, 2020
May 31, 2021
May 31, 2020
Goodwill And Intangible Assets Disclosure [Abstract]        
Amortization expense $ 2.9 $ 2.7 $ 8.5 $ 8.2
Future amortization expense, 2021 11.6   11.6  
Future amortization expense, 2022 8.3   8.3  
Future amortization expense, 2023 6.9   6.9  
Future amortization expense, 2024 6.7   6.7  
Future amortization expense, 2025 $ 5.8   $ 5.8