Question

The approximate value of (33)^1/5 is

Options

• 2.0125

• 2.1

• 2.01

• none of these

Answer 1

 2.0125
Consider the function y= f (x)=\[x^\frac{1}{5}\] .

\[\text { Let }: \]

\[ x = 32\]

\[ x + ∆ x = 33\]

\[ \Rightarrow ∆ x = 1\]

\[y = \left( x \right)^\frac{1}{5} \]

\[\text { For }x = 32, \]

\[y = 2\]

\[\text { Also }, \frac{dy}{dx} = \frac{1}{5 \left( x \right)^\frac{4}{5}}\]

\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 32} = \frac{1}{80}\]

\[ \Rightarrow ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{80} \times 1 = 0 . 0125\]

\[ \therefore \left( 33 \right)^\frac{1}{5} = y + ∆ y = 2 . 0125\]