Question

The approximate value of (33)^1/5 is
(a) 2.0125
(b) 2.1
(c) 2.01
(d) none of these

Answer 1

(a) 2.0125
Consider the function y= f(x)=$x^{\frac{1}{5}}$.
^{$$\begin{gathered} \mathrm{Let}: \\ x=32 \\ x+∆x=33 \\ \Rightarrow ∆x=1 \\ y={\left(x\right)}^{\frac{1}{5}} \\ \mathrm{For}x=32, \\ y=2 \\ \mathrm{Also},\frac{dy}{dx}=\frac{1}{5{\left(x\right)}^{\frac{4}{5}}} \\ \Rightarrow {\left(\frac{dy}{dx}\right)}_{x=32}=\frac{1}{80} \\ \Rightarrow ∆y=dy=\frac{dy}{dx}dx=\frac{1}{80}\times 1=0.0125 \\ \therefore {\left(33\right)}^{\frac{1}{5}}=y+∆y=2.0125 \end{gathered}$$}