Question

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

• A. 5.0267
• B. 5.4267
• C. 5.5267
• D. 5.001

Answer 1

Answer: (A)

5.0267

Answer 2

Let y = x^1/3, x = 125 and x + ∆x = 127. Then,

$\frac{dy}{dx}$ = $\frac{1}{3x^{2/3}}$ and ∆x = 2

When, x = 125, we have

y = 5 and $\frac{dy}{dx}$ = $\frac{1}{75}$

∴ ∆y = $\frac{dy}{dx}$ ∆x ⇒ ∆y = $\frac{1}{75}$× 2 = $\frac{2}{75}$

∴ (127)^1/3 = y + ∆y ⇒ 5 + $\frac{2}{75}$ ⇒ 5 + $\frac{8}{3}$ ×$\frac{1}{100}$

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

Hence (1) is the correct answer.