An approximate value of $\sqrt[4]{18}$ is

An approximate value of $\sqrt[4]{18}$ is
  1. 2.0512
  2. 2.0425
  3. 2.0625
  4. 2.0834

Solution

Let $y=f(x)=x^{1 / 4}$ and $x=16$ and $\Delta x=2$ So, $\Delta y=\left(\frac{d y}{d x}\right) \Delta x=\frac{1}{4}\left(x^{-3 / 4}\right) \Delta x$ at $\quad x=16$ and $\Delta x=2$ $ \Delta y=\frac{1}{4} \times \frac{1}{8} \times 2=\frac{1}{16} \text { and } y=(16)^{1 / 4}=2 $ So, $\quad y+\Delta y=2+\frac{1}{16}=2.0625$

Asked in: AP EAMCET 2018 (23 Apr Shift 2)

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