Simplify 2 square root of 3(3- square root of 2)

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

Apply the distributive property.

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

Multiply $3$ by $2$ .

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

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

Multiply $- 1$ by $2$ .

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

Combine using the product rule for radicals.

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

Multiply $2$ by $3$ .

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

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$5.49332535 \dots$

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