Simplify (2+ square root of 3)(6- square root of 2)

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

Step 1

Expand $(2 + \sqrt{3}) (6 - \sqrt{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify each term.

Multiply $2$ by $6$ .

$12 + 2 (- \sqrt{2}) + \sqrt{3} \cdot 6 + \sqrt{3} (- \sqrt{2})$

Multiply $- 1$ by $2$ .

$12 - 2 \sqrt{2} + \sqrt{3} \cdot 6 + \sqrt{3} (- \sqrt{2})$

Move $6$ to the left of $\sqrt{3}$ .

$12 - 2 \sqrt{2} + 6 \cdot \sqrt{3} + \sqrt{3} (- \sqrt{2})$

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

Combine using the product rule for radicals.

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

Multiply $3$ by $2$ .

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$17.11438797 \dots$