1. The problem is to verify if the equation $$\sqrt{3} + 2\sqrt{2}\sqrt{3} + \sqrt{2} = \sqrt{5} + \sqrt{24}$$ is correct. 2. First, simplify each term on the left side: - $$\sqrt{3}$$ remains as is. - $$2\sqrt{2}\sqrt{3} = 2\sqrt{2 \times 3} = 2\sqrt{6}$$. - $$\sqrt{2}$$ remains as is. So the left side becomes $$\sqrt{3} + 2\sqrt{6} + \sqrt{2}$$. 3. Now simplify the right side: - $$\sqrt{5}$$ remains as is. - $$\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}$$. So the right side becomes $$\sqrt{5} + 2\sqrt{6}$$. 4. Compare both sides: - Left side: $$\sqrt{3} + 2\sqrt{6} + \sqrt{2}$$ - Right side: $$\sqrt{5} + 2\sqrt{6}$$ 5. Since $$\sqrt{3} + \sqrt{2} \neq \sqrt{5}$$, the two sides are not equal. Final answer: The equation is incorrect.