1. The problem involves simplifying and performing operations on expressions involving square roots as given in a puzzle format. 2. Let's examine each expression step by step. 3. Expression: $3\sqrt{2} - ? = -10\sqrt{2}$ To find the missing term, solve for it: $$3\sqrt{2} - x = -10\sqrt{2} \implies x = 3\sqrt{2} + 10\sqrt{2} = 13\sqrt{2}$$ 4. Expression: $5\sqrt{6} + ? = -20\sqrt{6}$ Solve for the missing term: $$5\sqrt{6} + y = -20\sqrt{6} \implies y = -20\sqrt{6} - 5\sqrt{6} = -25\sqrt{6}$$ 5. The partial equation: $6\sqrt{2} + ? = ?$ There is not enough information to find specific values here without additional context. 6. Expression: $64\sqrt{5} - ? = ?$ Similarly, no explicit values are given for missing parts. 7. Based on the table, note the expressions: $6\sqrt{5}$, $6\sqrt{2}$, $5\sqrt{2}$, $10\sqrt{6}$, and $-20\sqrt{6}$ with operations $+, -, =$. 8. The last row expression appears as: $3\sqrt{2} - = -10\sqrt{2} = 5\sqrt{6} + + + -24\sqrt{2}$, which is unclear without symbols placement. 9. Summary of found missing values: - Missing term in $3\sqrt{2} - ? = -10\sqrt{2}$ is $13\sqrt{2}$. - Missing term in $5\sqrt{6} + ? = -20\sqrt{6}$ is $-25\sqrt{6}$. 10. These completions align with typical arithmetic of radical expressions. Final answers: - $3\sqrt{2} - 13\sqrt{2} = -10\sqrt{2}$ - $5\sqrt{6} + (-25\sqrt{6}) = -20\sqrt{6}$