Algebra Examples

$\sqrt{18} (2 + \sqrt{6}) - 2 \sqrt{3}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $9$ out of $18$ .

$\sqrt{9 (2)} (2 + \sqrt{6}) - 2 \sqrt{3}$

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 1.3

Apply the distributive property.

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

Step 1.4

Multiply $2$ by $3$ .

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

Step 1.5

Multiply $3 \sqrt{2} \sqrt{6}$ .

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Step 1.5.1

Combine using the product rule for radicals.

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

Step 1.5.2

Multiply $6$ by $2$ .

$6 \sqrt{2} + 3 \sqrt{12} - 2 \sqrt{3}$

Step 1.6

Simplify each term.

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Step 1.6.1

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

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Step 1.6.1.1

Factor $4$ out of $12$ .

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

Step 1.6.1.2

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

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

Step 1.6.2

Pull terms out from under the radical.

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

Step 1.6.3

Multiply $2$ by $3$ .

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

Step 2

Subtract $2 \sqrt{3}$ from $6 \sqrt{3}$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$15.41348460 \dots$