Evaluate ( square root of -81)/( square root of 3)

$\frac{\sqrt{- 81}}{\sqrt{3}}$

Pull out imaginary unit $i$ .

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Rewrite $- 81$ as $- 1 (81)$ .

$\frac{\sqrt{- 1 (81)}}{\sqrt{3}}$

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{81}}{\sqrt{3}}$

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{i \cdot \sqrt{81}}{\sqrt{3}}$

Combine $\sqrt{81}$ and $\sqrt{3}$ into a single radical.

$i \cdot \sqrt{\frac{81}{3}}$

Divide $81$ by $3$ .

$i \cdot \sqrt{27}$

Rewrite $27$ as $3^{2} \cdot 3$ .

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Factor $9$ out of $27$ .

$i \cdot \sqrt{9 (3)}$

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2} \cdot 3}$

Pull terms out from under the radical.

$i \cdot (3 \sqrt{3})$

Move $3$ to the left of $i$ .

$3 i \sqrt{3}$

Evaluate ( square root of -81)/( square root of 3)

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