Simplify ( square root of 108-6 square root of 3)^2

${(\sqrt{108} - 6 \sqrt{3})}^{2}$

Simplify each term.

Rewrite $108$ as $6^{2} \cdot 3$ .

Factor $36$ out of $108$ .

${(\sqrt{36 (3)} - 6 \sqrt{3})}^{2}$

Rewrite $36$ as $6^{2}$ .

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

Pull terms out from under the radical.

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

Simplify by adding terms.

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

$0^{2}$

Raising $0$ to any positive power yields $0$ .

$0$