Question

What is the approximate value of $\sqrt[5]{5242.999}$?

• A. $\frac{1214999}{405000}$
• B. $\frac{1115}{405}$
• C. $\frac{121499}{40500}$
• D. $\frac{1214999}{4050}$

Answer 1

Answer: (A)

$\frac{1214999}{405000}$

$f(x_0-\Delta x)=f\left(x\right){|}_{x_0}-f^{{}^{\prime }}\left(x\right){|}_{x_0}\Delta x$

$f\left(x\right)=\sqrt[5]{5x}$

$f^{{}^{\prime }}\left(x\right)=\frac{1}{5}\frac{1}{x^{\frac{4}{5}}}$

$f(243-0.001)=f\left(243\right)-f^{{}^{\prime }}\left(243\right)\left(0.001\right)$

$=\sqrt[5]{52}43-\frac{1}{5}\frac{1}{{243}^{\frac{4}{5}}}\left(0.001\right)$

$=3-\frac{1}{5}\frac{1}{81}\left(0.001\right)$

$=\frac{1215-0.001}{405}$

$=\frac{1214.999}{405}$

$=\frac{1214999}{405000}$

Hence, the answer is option (A).