Algebra Examples

$\sqrt{3} (\sqrt{6} + \sqrt{8})$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $8$ .

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

Step 1.1.2

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

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

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

Step 1.2

Pull terms out from under the radical.

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

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

Step 2

Simplify terms.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Combine using the product rule for radicals.

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

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

Step 3

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

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Step 3.1

Combine using the product rule for radicals.

$\sqrt{3 \cdot 6} + 2 \sqrt{3 \cdot 2}$

Step 3.2

Multiply $3$ by $2$ .

$\sqrt{3 \cdot 6} + 2 \sqrt{6}$

$\sqrt{3 \cdot 6} + 2 \sqrt{6}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $6$ .

$\sqrt{18} + 2 \sqrt{6}$

Step 4.2

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

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Step 4.2.1

Factor $9$ out of $18$ .

$\sqrt{9 (2)} + 2 \sqrt{6}$

Step 4.2.2

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

$\sqrt{3^{2} \cdot 2} + 2 \sqrt{6}$

$\sqrt{3^{2} \cdot 2} + 2 \sqrt{6}$

Step 4.3

Pull terms out from under the radical.

$3 \sqrt{2} + 2 \sqrt{6}$

$3 \sqrt{2} + 2 \sqrt{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2} + 2 \sqrt{6}$

Decimal Form:

$9.14162017 \dots$

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