Question

What is approximate value of $\sqrt[5]{242.999}?$

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

Answer 1

Answer: (C)

$\sqrt[5]{242.999}$
Let $f(x)=x^{1/5}$
$f(a+h)=f(a)+h{f}^{\prime }(a)f^{\prime }(x)=\frac{1}{5}{x}^{-\frac{4}{5}}$
$a=243,h=0.001$
$f(243-0.001)=(243{)}^{\frac{1}{5}}-(0.001)\frac{1}{5}(243{)}^{-\frac{4}{5}}$
$f(242.999)=3-\frac{1}{1000}\times \frac{1}{5}\times \frac{1}{81}$
$=3-\frac{1}{405000}=\frac{1214999}{405000}$