Algebra Examples

$3 \sqrt{- 18} + 5 \sqrt{- 12}$

Step 1

Rewrite $- 18$ as $- 1 (18)$ .

$3 \sqrt{- 1 (18)} + 5 \sqrt{- 12}$

Step 2

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$3 (\sqrt{- 1} \cdot \sqrt{18}) + 5 \sqrt{- 12}$

Step 3

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

$3 (i \cdot \sqrt{18}) + 5 \sqrt{- 12}$

Step 4

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

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Step 4.1

Factor $9$ out of $18$ .

$3 (i \cdot \sqrt{9 (2)}) + 5 \sqrt{- 12}$

Step 4.2

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

$3 (i \cdot \sqrt{3^{2} \cdot 2}) + 5 \sqrt{- 12}$

Step 5

Pull terms out from under the radical.

$3 (i \cdot (3 \sqrt{2})) + 5 \sqrt{- 12}$

Step 6

Move $3$ to the left of $i$ .

$3 (3 \cdot i \sqrt{2}) + 5 \sqrt{- 12}$

Step 7

Multiply $3$ by $3$ .

$9 (i \sqrt{2}) + 5 \sqrt{- 12}$

Step 8

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

$9 i \sqrt{2} + 5 \sqrt{- 1 (12)}$

Step 9

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

$9 i \sqrt{2} + 5 (\sqrt{- 1} \cdot \sqrt{12})$

Step 10

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

$9 i \sqrt{2} + 5 (i \cdot \sqrt{12})$

Step 11

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

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Step 11.1

Factor $4$ out of $12$ .

$9 i \sqrt{2} + 5 (i \cdot \sqrt{4 (3)})$

Step 11.2

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

$9 i \sqrt{2} + 5 (i \cdot \sqrt{2^{2} \cdot 3})$

Step 12

Pull terms out from under the radical.

$9 i \sqrt{2} + 5 (i \cdot (2 \sqrt{3}))$

Step 13

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

$9 i \sqrt{2} + 5 (2 \cdot i \sqrt{3})$

Step 14

Multiply $2$ by $5$ .

$9 i \sqrt{2} + 10 i \sqrt{3}$