Simplify (-9 square root of -24)(7 square root of -12)

$(- 9 \sqrt{- 24}) (7 \sqrt{- 12})$

Rewrite $- 24$ as $- 1 (24)$ .

$- 9 \sqrt{- 1 (24)} (7 \sqrt{- 12})$

Rewrite $\sqrt{- 1 (24)}$ as $\sqrt{- 1} \cdot \sqrt{24}$ .

$- 9 (\sqrt{- 1} \cdot \sqrt{24}) (7 \sqrt{- 12})$

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

$- 9 (i \cdot \sqrt{24}) (7 \sqrt{- 12})$

Rewrite $- 12$ as $- 1 (12)$ .

$- 9 (i \cdot \sqrt{24}) (7 \sqrt{- 1 (12)})$

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$- 9 (i \cdot \sqrt{24}) (7 (\sqrt{- 1} \cdot \sqrt{12}))$

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

$- 9 (i \cdot \sqrt{24}) (7 (i \cdot \sqrt{12}))$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$- 9 (i \cdot \sqrt{4 (6)}) (7 (i \cdot \sqrt{12}))$

Rewrite $4$ as $2^{2}$ .

$- 9 (i \cdot \sqrt{2^{2} \cdot 6}) (7 (i \cdot \sqrt{12}))$

Pull terms out from under the radical.

$- 9 (i \cdot (2 \sqrt{6})) (7 (i \cdot \sqrt{12}))$

Simplify the expression.

Move $2$ to the left of $i$ .

$- 9 (2 \cdot i \sqrt{6}) (7 (i \cdot \sqrt{12}))$

Multiply $2$ by $- 9$ .

$- 18 (i \sqrt{6}) (7 (i \cdot \sqrt{12}))$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$- 18 i \sqrt{6} (7 (i \cdot \sqrt{4 (3)}))$

Rewrite $4$ as $2^{2}$ .

$- 18 i \sqrt{6} (7 (i \cdot \sqrt{2^{2} \cdot 3}))$

Pull terms out from under the radical.

$- 18 i \sqrt{6} (7 (i \cdot (2 \sqrt{3})))$

Simplify the expression.

Move $2$ to the left of $i$ .

$- 18 i \sqrt{6} (7 (2 \cdot i \sqrt{3}))$

Multiply $2$ by $7$ .

$- 18 i \sqrt{6} (14 (i \sqrt{3}))$

Multiply $- 18 i \sqrt{6} (14 i \sqrt{3})$ .

Multiply $14$ by $- 18$ .

$- 252 i \sqrt{6} (i \sqrt{3})$

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

$- 252 (i^{1} i) \sqrt{6} \sqrt{3}$

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

$- 252 (i^{1} i^{1}) \sqrt{6} \sqrt{3}$

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

$- 252 i^{1 + 1} \sqrt{6} \sqrt{3}$

Add $1$ and $1$ .

$- 252 i^{2} \sqrt{6} \sqrt{3}$

Combine using the product rule for radicals.

$- 252 i^{2} \sqrt{3 \cdot 6}$

Multiply $3$ by $6$ .

$- 252 i^{2} \sqrt{18}$

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

$- 252 \cdot - 1 \sqrt{18}$

Multiply $- 252$ by $- 1$ .

$252 \sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$252 \sqrt{9 (2)}$

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

$252 \sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$252 (3 \sqrt{2})$

Multiply $3$ by $252$ .

$756 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$756 \sqrt{2}$

Decimal Form:

$1069.14545315 \dots$

Simplify (-9 square root of -24)(7 square root of -12)

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