Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

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

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Step 7.1

Factor $4$ out of $24$ .

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

Step 7.2

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Simplify the expression.

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Step 9.1

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

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

Step 9.2

Multiply $2$ by $- 9$ .

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

Step 10

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

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Step 10.1

Factor $4$ out of $12$ .

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

Step 10.2

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

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

Step 11

Pull terms out from under the radical.

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

Step 12

Simplify the expression.

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Step 12.1

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

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

Step 12.2

Multiply $2$ by $7$ .

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

Step 13

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

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Step 13.1

Multiply $14$ by $- 18$ .

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

Step 13.2

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

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

Step 13.3

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

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

Step 13.4

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

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

Step 13.5

Add $1$ and $1$ .

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

Step 13.6

Combine using the product rule for radicals.

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

Step 13.7

Multiply $3$ by $6$ .

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

Step 14

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

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

Step 15

Multiply $- 252$ by $- 1$ .

$252 \sqrt{18}$

Step 16

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

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Step 16.1

Factor $9$ out of $18$ .

$252 \sqrt{9 (2)}$

Step 16.2

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

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

Step 17

Pull terms out from under the radical.

$252 (3 \sqrt{2})$

Step 18

Multiply $3$ by $252$ .

$756 \sqrt{2}$

Step 19

The result can be shown in multiple forms.

Exact Form:

$756 \sqrt{2}$

Decimal Form:

$1069.14545315 \dots$