The expression \( 6 \cdot \sqrt{3} \) represents the product of a rational number (6) and an irrational number (\(\sqrt{3}\)). The result of this product, \( 6 \cdot \sqrt{3} \), is an irrational number.
So, the completed statements are: The product of \( 6 \cdot \sqrt{3} \) represents the product of a rational number and an irrational number. The result of the product of \( 6 \cdot \sqrt{3} \) is an irrational number.