Algebra Examples

$(- \sqrt{- 1}) (- \sqrt{- 24})$

Step 1

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

$- i (- \sqrt{- 24})$

Step 2

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

$- i (- \sqrt{- 1 (24)})$

Step 3

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

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

Step 4

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

$- i (- (i \cdot \sqrt{24}))$

Step 5

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

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Step 5.1

Factor $4$ out of $24$ .

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

Step 5.2

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Simplify the expression.

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Step 7.1

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

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

Step 7.2

Multiply $2$ by $- 1$ .

$- i (- 2 (i \sqrt{6}))$

Step 8

Multiply $- i (- 2 i \sqrt{6})$ .

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Step 8.1

Multiply $- 2$ by $- 1$ .

$2 i (i \sqrt{6})$

Step 8.2

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

$2 (i^{1} i) \sqrt{6}$

Step 8.3

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

$2 (i^{1} i^{1}) \sqrt{6}$

Step 8.4

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

$2 i^{1 + 1} \sqrt{6}$

Step 8.5

Add $1$ and $1$ .

$2 i^{2} \sqrt{6}$

Step 9

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

$2 \cdot - 1 \sqrt{6}$

Step 10

Multiply $2$ by $- 1$ .

$- 2 \sqrt{6}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{6}$

Decimal Form:

$- 4.89897948 \dots$