Finite Math Examples

$(4 \sqrt{- 13}) - (10 \sqrt{- 12})$

Step 1

Rewrite $- 13$ as $- 1 (13)$ .

$4 \sqrt{- 1 (13)} - (10 \sqrt{- 12})$

Step 2

Rewrite $\sqrt{- 1 (13)}$ as $\sqrt{- 1} \cdot \sqrt{13}$ .

$4 (\sqrt{- 1} \cdot \sqrt{13}) - (10 \sqrt{- 12})$

Step 3

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

$4 (i \cdot \sqrt{13}) - (10 \sqrt{- 12})$

Step 4

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

$4 i \sqrt{13} - (10 \sqrt{- 1 (12)})$

Step 5

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

$4 i \sqrt{13} - (10 (\sqrt{- 1} \cdot \sqrt{12}))$

Step 6

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

$4 i \sqrt{13} - (10 (i \cdot \sqrt{12}))$

Step 7

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

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Step 7.1

Factor $4$ out of $12$ .

$4 i \sqrt{13} - (10 (i \cdot \sqrt{4 (3)}))$

Step 7.2

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

$4 i \sqrt{13} - (10 (i \cdot \sqrt{2^{2} \cdot 3}))$

Step 8

Pull terms out from under the radical.

$4 i \sqrt{13} - (10 (i \cdot (2 \sqrt{3})))$

Step 9

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

$4 i \sqrt{13} - (10 (2 \cdot i \sqrt{3}))$

Step 10

Multiply $2$ by $10$ .

$4 i \sqrt{13} - (20 (i \sqrt{3}))$

Step 11

Multiply $20$ by $- 1$ .

$4 i \sqrt{13} - 20 i \sqrt{3}$