Income Taxes - Summary of Difference Between the Federal Statutory Rate and the Company's Effective Tax Rate (Details)	12 Months Ended
Aug. 31, 2021	Aug. 31, 2020	Aug. 31, 2019
Reconciliation of the difference between the federal statutory rate and the Company's effective tax rate [Abstract]
Federal statutory rate	21.00%	21.00%	21.00%
State taxes, net of credits	1.40%	(57.90%)	1.20%
Foreign income taxed at different rates	(0.50%)	(11.60%)	(0.20%)
Valuation allowance on deferred tax assets	(1.00%)	(24.50%)	(0.20%)
Federal rate change	0.40%	71.90%
Non-deductible officers’ compensation	1.20%	(46.90%)	1.80%
Other non-deductible expenses	0.40%	(66.00%)	1.00%
Noncontrolling interests	(0.50%)	21.10%	(0.50%)
Research and development credits	(1.50%)	99.30%	(0.50%)
Tax return to provision adjustment		89.20%	0.50%
Unrecognized tax benefits	0.90%	(97.30%)	0.70%
Interest income	(0.10%)	9.00%	(0.40%)
Excess tax benefit from stock-based compensation	(0.20%)	3.00%	(1.20%)
Foreign derived intangible income	(2.50%)
Other	(0.80%)	(18.90%)
Effective tax rate	18.20%	(8.60%)	23.20%

Effective income tax rate reconciliation foreign derived intangible income.

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Effective income tax rate reconciliation interest income (expense).

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Effective Income Tax Rate Reconciliation, Nondeductible Expense Officers Compensation, Percent

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Effective income tax rate reconciliation tax return to provision adjustment percent.

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Effective Income Tax Rate Reconciliation, Unrecognized Tax Benefits, Percent

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Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

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Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 740
-SubTopic 10
-Section 50
-Paragraph 12
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Percentage of domestic federal statutory tax rate applicable to pretax income (loss).

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Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to changes in the valuation allowance for deferred tax assets.

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Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to statutory income tax expense (benefit) outside of the country of domicile.

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Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to noncontrolling interest income (loss) exempt from income taxes.

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Percentage of difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operation, attributable to expense for award under share-based payment arrangement. Excludes expense determined to be nondeductible upon grant or after for award under share-based payment arrangement.

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Percentage of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations applicable to state and local income tax expense (benefit), net of federal tax expense (benefit).

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