Rewrite <math><mstyle displaystyle="true"><mo>-</mo><mn>81</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>81</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mn>81</mn><mo>)</mo></mrow></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt><mo>⋅</mo><msqrt><mn>81</mn></msqrt></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><msqrt><mo>-</mo><mn>1</mn></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>81</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>9</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

Move <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>i</mi></mstyle></math> .

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