Algebra Examples

$\sqrt{- 10} \cdot \sqrt{- 24}$

Step 1

Rewrite $- 10$ as $- 1 (10)$ .

$\sqrt{- 1 (10)} \cdot \sqrt{- 24}$

Step 2

Rewrite $\sqrt{- 1 (10)}$ as $\sqrt{- 1} \cdot \sqrt{10}$ .

$\sqrt{- 1} \cdot \sqrt{10} \cdot \sqrt{- 24}$

Step 3

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

$i \cdot \sqrt{10} \cdot \sqrt{- 24}$

Step 4

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

$i \cdot \sqrt{10} \cdot \sqrt{- 1 (24)}$

Step 5

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

$i \cdot \sqrt{10} \cdot (\sqrt{- 1} \cdot \sqrt{24})$

Step 6

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

$i \cdot \sqrt{10} \cdot (i \cdot \sqrt{24})$

Step 7

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

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Step 7.1

Factor $4$ out of $24$ .

$i \sqrt{10} \cdot (i \cdot \sqrt{4 (6)})$

Step 7.2

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

$i \sqrt{10} \cdot (i \cdot \sqrt{2^{2} \cdot 6})$

Step 8

Pull terms out from under the radical.

$i \sqrt{10} \cdot (i \cdot (2 \sqrt{6}))$

Step 9

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

$i \sqrt{10} \cdot (2 \cdot i \sqrt{6})$

Step 10

Multiply $i \sqrt{10} (2 i \sqrt{6})$ .

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Step 10.1

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

$\sqrt{10} (2 (i^{1} i) \sqrt{6})$

Step 10.2

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

$\sqrt{10} (2 (i^{1} i^{1}) \sqrt{6})$

Step 10.3

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

$\sqrt{10} (2 i^{1 + 1} \sqrt{6})$

Step 10.4

Add $1$ and $1$ .

$\sqrt{10} (2 i^{2} \sqrt{6})$

Step 10.5

Combine using the product rule for radicals.

$2 i^{2} \sqrt{10 \cdot 6}$

Step 10.6

Multiply $10$ by $6$ .

$2 i^{2} \sqrt{60}$

Step 11

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

$2 \cdot - 1 \sqrt{60}$

Step 12

Multiply $2$ by $- 1$ .

$- 2 \sqrt{60}$

Step 13

Rewrite $60$ as $2^{2} \cdot 15$ .

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Step 13.1

Factor $4$ out of $60$ .

$- 2 \sqrt{4 (15)}$

Step 13.2

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

$- 2 \sqrt{2^{2} \cdot 15}$

Step 14

Pull terms out from under the radical.

$- 2 (2 \sqrt{15})$

Step 15

Multiply $2$ by $- 2$ .

$- 4 \sqrt{15}$

Step 16

The result can be shown in multiple forms.

Exact Form:

$- 4 \sqrt{15}$

Decimal Form:

$- 15.49193338 \dots$