Simplify (6 square root of -7)( square root of -3)

$(6 \sqrt{- 7}) (\sqrt{- 3})$

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

$6 \sqrt{- 1 (7)} \sqrt{- 3}$

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

$6 (\sqrt{- 1} \cdot \sqrt{7}) \sqrt{- 3}$

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

$6 (i \cdot \sqrt{7}) \sqrt{- 3}$

Rewrite $- 3$ as $- 1 (3)$ .

$6 (i \cdot \sqrt{7}) \sqrt{- 1 (3)}$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$6 (i \cdot \sqrt{7}) (\sqrt{- 1} \cdot \sqrt{3})$

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

$6 (i \cdot \sqrt{7}) (i \cdot \sqrt{3})$

Multiply $6 i \sqrt{7} (i \sqrt{3})$ .

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

$6 (i^{1} i) \sqrt{7} \sqrt{3}$

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

$6 (i^{1} i^{1}) \sqrt{7} \sqrt{3}$

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

$6 i^{1 + 1} \sqrt{7} \sqrt{3}$

Add $1$ and $1$ .

$6 i^{2} \sqrt{7} \sqrt{3}$

Combine using the product rule for radicals.

$6 i^{2} \sqrt{3 \cdot 7}$

Multiply $3$ by $7$ .

$6 i^{2} \sqrt{21}$

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

$6 \cdot - 1 \sqrt{21}$

Multiply $6$ by $- 1$ .

$- 6 \sqrt{21}$

The result can be shown in multiple forms.

Exact Form:

$- 6 \sqrt{21}$

Decimal Form:

$- 27.49545416 \dots$