Question

The approximate value of $(10{)}^{1/3}$ upto four places of decimal, is

• A. $2.1547$
• B. $2.1545$
• C. $2.1544$
• D. None of these

Answer 1

The correct option is D None of these

We have,

$(10{)}^{1/3}=(8+2{)}^{1/3}$

Also, $8^{1/3}=2$

Let $y=x^{1/3}$

$y\left(8\right)=(8{)}^{1/3}=2$

Now, $\frac{△y}{△x}=\frac{1}{3}{x}^{-2/3}$

$\frac{y\left(10\right)-y\left(8\right)}{10-8}=\frac{1}{3}{8}^{-2/3}$

$\frac{y\left(10\right)-2}{2}=\frac{1}{3}.\frac{1}{4}$

$y\left(10\right)=2+\frac{1}{6}=\frac{13}{6}=2.1666$

Hence, option D is correct.