Simplify ( square root of 3-7)(8+ square root of 3)

$(\sqrt{3} - 7) (8 + \sqrt{3})$

Expand $(\sqrt{3} - 7) (8 + \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$\sqrt{3} (8 + \sqrt{3}) - 7 (8 + \sqrt{3})$

Apply the distributive property.

$\sqrt{3} \cdot 8 + \sqrt{3} \sqrt{3} - 7 (8 + \sqrt{3})$

Apply the distributive property.

$\sqrt{3} \cdot 8 + \sqrt{3} \sqrt{3} - 7 \cdot 8 - 7 \sqrt{3}$

Simplify and combine like terms.

Simplify each term.

Move $8$ to the left of $\sqrt{3}$ .

$8 \cdot \sqrt{3} + \sqrt{3} \sqrt{3} - 7 \cdot 8 - 7 \sqrt{3}$

Combine using the product rule for radicals.

$8 \sqrt{3} + \sqrt{3 \cdot 3} - 7 \cdot 8 - 7 \sqrt{3}$

Multiply $3$ by $3$ .

$8 \sqrt{3} + \sqrt{9} - 7 \cdot 8 - 7 \sqrt{3}$

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

$8 \sqrt{3} + \sqrt{3^{2}} - 7 \cdot 8 - 7 \sqrt{3}$

Pull terms out from under the radical, assuming positive real numbers.

$8 \sqrt{3} + 3 - 7 \cdot 8 - 7 \sqrt{3}$

Multiply $- 7$ by $8$ .

$8 \sqrt{3} + 3 - 56 - 7 \sqrt{3}$

Subtract $7 \sqrt{3}$ from $8 \sqrt{3}$ .

$3 - 56 + \sqrt{3}$

Subtract $56$ from $3$ .

$- 53 + \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$- 53 + \sqrt{3}$

Decimal Form:

$- 51.26794919 \dots$