\( \sqrt{2 c} \cdot \sqrt{3 c} \) ssume that the variable represents a positive real number.

Did you know that when you multiply square roots, you can combine them under a single square root symbol? So, \( \sqrt{2c} \cdot \sqrt{3c} \) becomes \( \sqrt{(2c) \cdot (3c)} \), which simplifies to \( \sqrt{6c^2} \). This means you can actually take the square root of \( c^2 \) outside of the radical, leading to \( c \sqrt{6} \). Now let’s tackle the common mistake: people often forget to multiply the coefficients correctly. In our case, \( 2 \) and \( 3 \) need to be multiplied together first, resulting in \( 6 \). If someone were to miss that, they could end up with incorrect coefficients or make errors when simplifying! Remember, it's all about keeping those numbers straight!