Linear Algebra Examples

$\sqrt{- 14} \sqrt{- 2}$

Step 1

Rewrite $- 14$ as $- 1 (14)$ .

$\sqrt{- 1 (14)} \sqrt{- 2}$

Step 2

Rewrite $\sqrt{- 1 (14)}$ as $\sqrt{- 1} \cdot \sqrt{14}$ .

$\sqrt{- 1} \cdot \sqrt{14} \sqrt{- 2}$

Step 3

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

$i \cdot \sqrt{14} \sqrt{- 2}$

Step 4

Rewrite $- 2$ as $- 1 (2)$ .

$i \cdot \sqrt{14} \sqrt{- 1 (2)}$

Step 5

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$i \cdot \sqrt{14} (\sqrt{- 1} \cdot \sqrt{2})$

Step 6

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

$i \cdot \sqrt{14} (i \cdot \sqrt{2})$

Step 7

Multiply $i \sqrt{14} (i \sqrt{2})$ .

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Step 7.1

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

$i^{1} i \sqrt{14} \sqrt{2}$

Step 7.2

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

$i^{1} i^{1} \sqrt{14} \sqrt{2}$

Step 7.3

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

$i^{1 + 1} \sqrt{14} \sqrt{2}$

Step 7.4

Add $1$ and $1$ .

$i^{2} \sqrt{14} \sqrt{2}$

Step 7.5

Combine using the product rule for radicals.

$i^{2} \sqrt{2 \cdot 14}$

Step 7.6

Multiply $2$ by $14$ .

$i^{2} \sqrt{28}$

Step 8

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

$- 1 \sqrt{28}$

Step 9

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 9.1

Factor $4$ out of $28$ .

$- 1 \sqrt{4 (7)}$

Step 9.2

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

$- 1 \sqrt{2^{2} \cdot 7}$

Step 10

Pull terms out from under the radical.

$- 1 (2 \sqrt{7})$

Step 11

Multiply $2$ by $- 1$ .

$- 2 \sqrt{7}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{7}$

Decimal Form:

$- 5.29150262 \dots$