TS EAMCET · Maths · Application of Derivatives
The nearest approximate value of \(\sqrt{2023}\) is
- A \((6.6)^2\)
- B \(44.9778\)
- C \((6.8)^2\)
- D \(44.7777\)
Answer & Solution
Correct Answer
(B) \(44.9778\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text 2023 < 2025 \Rightarrow \sqrt{2023} < \sqrt{2025} \\ & \Rightarrow \sqrt{2023} < 45 \\ & \therefore \sqrt{2023}=\sqrt{2025-2} \approx \sqrt{2025}-\frac{2}{2 \sqrt{2025}+1} \\ & \quad \approx 45-\frac{2}{91} \approx 45-0.222 \approx 44.9778 .\end{aligned}
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