1. **State the problem:** Simplify fully the expression $\sqrt{3} (\sqrt{27} + \sqrt{3})$. 2. **Recall the properties of square roots:** - $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ - Simplify square roots by factoring out perfect squares. 3. **Simplify inside the parentheses:** - $\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}$ 4. **Rewrite the expression:** $$\sqrt{3} (3\sqrt{3} + \sqrt{3})$$ 5. **Factor out $\sqrt{3}$ inside the parentheses:** $$\sqrt{3} (3\sqrt{3} + \sqrt{3}) = \sqrt{3} \times \sqrt{3} (3 + 1)$$ 6. **Simplify $\sqrt{3} \times \sqrt{3}$:** $$\sqrt{3} \times \sqrt{3} = \sqrt{3 \times 3} = \sqrt{9} = 3$$ 7. **Multiply the simplified terms:** $$3 \times (3 + 1) = 3 \times 4 = 12$$ **Final answer:** $$12$$