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Question 22

If $$a = \sqrt{(2025)^3 - (2023)^3}$$, the value of $$\sqrt{\frac{a^2-2}{6}}$$ is ------.


Correct Answer: 2024

Solution

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Since $$a^2 = 2025^3-2023^3 = (2024+1)^3-(2024-1)^3$$

$$a^2=2024^2+1+3*2024+3*(2024)^2-[2024^2-1+3*(2024)-3*(2024)^2]$$

$$a^2=6*(2024)^2+2$$

$$a^2-2=6*(2024)^2$$

$$\dfrac{a^2-2}{6}=2024^2$$

$$\sqrt{\dfrac{a^2-2}{6}}=2024$$

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