The value of (127)1/3 to four decimal places is

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Question

The value of

(127)^{1 / 3}

to four decimal places is

Options:

A . 5.0267

B . 5.4267

C . 5.5267

D . 5.001

Answer: Option A
:
A
Let y =

x^{1 / 3}, x = 125

and

x + Δ x = 127.

Then,

\frac{d y}{d x} = \frac{1}{3 x^{2 / 3}} a n d Δ x = 0

When, x = 125, we have

y = 5 a n d \frac{d y}{d x} = \frac{1}{75}

∴ y = \frac{d y}{d x} Δ x \Rightarrow Δ y \frac{1}{75} \times 2 = \frac{2}{75}

∴ (127)^{1 / 3} = y + Δ y = 5 + \frac{2}{75} = 5 + \frac{8}{3} \times \frac{1}{100}

\Rightarrow (127)^{1 / 3} = 5 + \frac{(2.6667)}{100} = 5.02667 = 5.0267

Hence (a) is the correct answer.

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