Algebra Examples

$\sqrt{8} (\sqrt{6} - \sqrt{12})$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2)} (\sqrt{6} - \sqrt{12})$

Step 1.2

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

$\sqrt{2^{2} \cdot 2} (\sqrt{6} - \sqrt{12})$

$\sqrt{2^{2} \cdot 2} (\sqrt{6} - \sqrt{12})$

Step 2

Pull terms out from under the radical.

$2 \sqrt{2} (\sqrt{6} - \sqrt{12})$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Factor $4$ out of $12$ .

$2 \sqrt{2} (\sqrt{6} - \sqrt{4 (3)})$

Step 3.1.2

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

$2 \sqrt{2} (\sqrt{6} - \sqrt{2^{2} \cdot 3})$

$2 \sqrt{2} (\sqrt{6} - \sqrt{2^{2} \cdot 3})$

Step 3.2

Pull terms out from under the radical.

$2 \sqrt{2} (\sqrt{6} - (2 \sqrt{3}))$

Step 3.3

Multiply $2$ by $- 1$ .

$2 \sqrt{2} (\sqrt{6} - 2 \sqrt{3})$

$2 \sqrt{2} (\sqrt{6} - 2 \sqrt{3})$

Step 4

Apply the distributive property.

$2 \sqrt{2} \sqrt{6} + 2 \sqrt{2} (- 2 \sqrt{3})$

Step 5

Multiply $2 \sqrt{2} \sqrt{6}$ .

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Step 5.1

Combine using the product rule for radicals.

$2 \sqrt{6 \cdot 2} + 2 \sqrt{2} (- 2 \sqrt{3})$

Step 5.2

Multiply $6$ by $2$ .

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

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

Step 6

Multiply $2 \sqrt{2} (- 2 \sqrt{3})$ .

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Step 6.1

Multiply $- 2$ by $2$ .

$2 \sqrt{12} - 4 \sqrt{2} \sqrt{3}$

Step 6.2

Combine using the product rule for radicals.

$2 \sqrt{12} - 4 \sqrt{3 \cdot 2}$

Step 6.3

Multiply $3$ by $2$ .

$2 \sqrt{12} - 4 \sqrt{6}$

$2 \sqrt{12} - 4 \sqrt{6}$

Step 7

Simplify each term.

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Step 7.1

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

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Step 7.1.1

Factor $4$ out of $12$ .

$2 \sqrt{4 (3)} - 4 \sqrt{6}$

Step 7.1.2

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

$2 \sqrt{2^{2} \cdot 3} - 4 \sqrt{6}$

$2 \sqrt{2^{2} \cdot 3} - 4 \sqrt{6}$

Step 7.2

Pull terms out from under the radical.

$2 (2 \sqrt{3}) - 4 \sqrt{6}$

Step 7.3

Multiply $2$ by $2$ .

$4 \sqrt{3} - 4 \sqrt{6}$

$4 \sqrt{3} - 4 \sqrt{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{3} - 4 \sqrt{6}$

Decimal Form:

$- 2.86975574 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$