The approximate value of (33)$\frac{1}{5}$ is

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2.0125 Consider the function y= f (x)=x^$\frac{1}{5}$ . \text { Let }: x = 32 x + ∆ x = 33 \Rightarrow ∆ x = 1 y = \left( x \right)^$\frac{1}{5}$ \text { For }x = 32, y = 2 \text { Also }, dy/dx = \frac{1}{5 \left( x \right)^$\frac{4}{5}$} \Rightarrow \left( dy/dx \right)_{x = 32} = $\frac{1}{80}$ \Rightarrow ∆ y = dy = dy/dxdx = $\frac{1}{80}$ $\times$ 1 = 0 . 0125 \therefore \left( 33 \right)^$\frac{1}{5}$ = y + ∆ y = 2 . 0125

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