Q105 / 180 · KCET 2019 · Mathematics

The value of \( \sqrt{24.99} \) is

  • A
    \( 4.899 \)
  • B
    \( 4.897 \)
  • Correct answer
    C
    \( 4.999 \)
  • D
    \( 5.001 \)

Solution

(C) \( \sqrt{24.99} \) \( \Delta y=f(x+\Delta x)-f(x)\left[\Delta y \approx \frac{d y}{d x} \times \Delta x\right] \) Take \( f(x)=\sqrt{x}\left[\approx \frac{1}{2 \sqrt{x}} \times-0.01\right] \) \( \Delta x=-0.01\left[\approx-\frac{0.01}{10}\right] \) \( \therefore f(24.99)=\sqrt{25}+\Delta y \) \( \approx 5-0.001 \) \( \approx 4.999 \)

Hence, the correct answer is option: 'C'.

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