Simplify square root of -7* square root of -11

$\sqrt{- 7} \cdot \sqrt{- 11}$

Rewrite $- 7$ as $- 1 (7)$ .

$\sqrt{- 1 (7)} \cdot \sqrt{- 11}$

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$\sqrt{- 1} \cdot \sqrt{7} \cdot \sqrt{- 11}$

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

$i \cdot \sqrt{7} \cdot \sqrt{- 11}$

Rewrite $- 11$ as $- 1 (11)$ .

$i \cdot \sqrt{7} \cdot \sqrt{- 1 (11)}$

Rewrite $\sqrt{- 1 (11)}$ as $\sqrt{- 1} \cdot \sqrt{11}$ .

$i \cdot \sqrt{7} \cdot (\sqrt{- 1} \cdot \sqrt{11})$

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

$i \cdot \sqrt{7} \cdot (i \cdot \sqrt{11})$

Multiply $i \sqrt{7} (i \sqrt{11})$ .

Raise $i$ to the power of $1$ .

$i^{1} i \sqrt{7} \sqrt{11}$

Raise $i$ to the power of $1$ .

$i^{1} i^{1} \sqrt{7} \sqrt{11}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$i^{1 + 1} \sqrt{7} \sqrt{11}$

Add $1$ and $1$ .

$i^{2} \sqrt{7} \sqrt{11}$

Combine using the product rule for radicals.

$i^{2} \sqrt{11 \cdot 7}$

Multiply $11$ by $7$ .

$i^{2} \sqrt{77}$

Rewrite $i^{2}$ as $- 1$ .

$- 1 \sqrt{77}$

Rewrite $- 1 \sqrt{77}$ as $- \sqrt{77}$ .

$- \sqrt{77}$

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{77}$

Decimal Form:

$- 8.77496438 \dots$