Question 1
The value of $$\sqrt{2023\sqrt{2022\sqrt{2021 \times 2019 + 1} + 1} + 1}$$ is
Solution
The innermost quantity is $$2021 \times 2019 + 1 = 2020^2$$, so its square root is $$2020$$. The next radical becomes $$\sqrt{2022 \times 2020 + 1} = \sqrt{2021^2} = 2021$$. Therefore, the complete expression is $$\sqrt{2023 \times 2021 + 1} = \sqrt{2022^2} = 2022$$.
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