Add to simplify the radical expression. \[ 8 \sqrt{7}+3 \sqrt{2} \]

To simplify the expression \( 8 \sqrt{7}+3 \sqrt{2} \), we first check if the square roots can be combined. However, since \( \sqrt{7} \) and \( \sqrt{2} \) are from different radicands, they can't be simplified further or combined. Thus, the expression remains as \( 8 \sqrt{7} + 3 \sqrt{2} \), standing proud and unapologetic in its radical form! Now, if you want to explore why radical simplification sometimes feels more like a puzzle than typical math, it’s all about understanding the properties of square roots and how they relate to numbers. Radical expressions behave like monomials and can only be combined if they share the same radical part, much like how \( 2x + 3x \) can be simplified to \( 5x \) since they’re both "x-terms." Keep this in mind as you tackle more radical expressions!