1. **State the problem:** We want to verify if the equation $$\sqrt{3} + 2\sqrt{2}\sqrt{3} + \sqrt{2} = \sqrt{5} + \sqrt{24}$$ is correct. 2. **Simplify the left side:** - Recall that $$\sqrt{a}\sqrt{b} = \sqrt{ab}$$. - So, $$2\sqrt{2}\sqrt{3} = 2\sqrt{6}$$. - The left side becomes $$\sqrt{3} + 2\sqrt{6} + \sqrt{2}$$. 3. **Simplify the right side:** - $$\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}$$. - 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. **Subtract $$2\sqrt{6}$$ from both sides:** - Left: $$\sqrt{3} + \sqrt{2}$$ - Right: $$\sqrt{5}$$ 6. **Check if $$\sqrt{3} + \sqrt{2} = \sqrt{5}$$:** - Square both sides: $$\left(\sqrt{3} + \sqrt{2}\right)^2 = (\sqrt{5})^2$$ - Left: $$3 + 2 + 2\sqrt{6} = 5 + 2\sqrt{6}$$ - Right: $$5$$ 7. Since $$5 + 2\sqrt{6} \neq 5$$, the equality does not hold. **Final answer:** The equation is **not correct**.