Evaluate 2 square root of 3( square root of 18- square root of 6)

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Trigonometry

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

Simplify each term.

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

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Factor $9$ out of $18$ .

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

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

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

Pull terms out from under the radical.

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

Apply the distributive property.

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

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

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Multiply $3$ by $2$ .

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

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

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

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

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Multiply $- 1$ by $2$ .

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

Combine using the product rule for radicals.

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

Multiply $6$ by $3$ .

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

Simplify each term.

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

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Factor $9$ out of $18$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 2$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$6.21165708 \dots$

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