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# Solution for Using Differential, Find the Approximate Value of the ( 33 ) 1 5 ? - CBSE (Science) Class 12 - Mathematics

#### Question

Using differential, find the approximate value of the $\left( 33 \right)^\frac{1}{5}$ ?

#### Solution

$\text { Consider the function y } = f\left( x \right) = \left( x \right)^\frac{1}{5} .$

$\text { Let }:$

$x = 32$

$x + ∆ x = 33$

$\text{Then },$

$∆ x = 1$

$\text { For } x = 33,$

$y = \left( 32 \right)^\frac{1}{5} = 2$

$\text { Let }:$

$dx = ∆ x = 1$

$\text { Now }, y = \left( x \right)^\frac{1}{5}$

$\Rightarrow \frac{dy}{dx} = \frac{1}{5 \left( x \right)^\frac{4}{5}}$

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

$\therefore ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{80} \times 1 = 0 . 0125$

$\Rightarrow ∆ y = 0 . 0125$

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

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 9.23 | Page no. 9

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Solution for question: Using Differential, Find the Approximate Value of the ( 33 ) 1 5 ? concept: Approximations. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
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