Question

Estimate the value of cube root of the number $1333$.

• A. $10.99$
• B. $20.10$
• C. $12.45$
• D. $10.56$

Answer 1

The correct option is A $10.99$

We need to find $\sqrt[3]{31333}$
Take, $n=1333$, choose any starting value of $x$.
So, ${11}^3$ is $1331<1333$
So, $x=11$
$x_{\text{next}}$ $=$ $\frac{2}{3}x+\frac{n}{3x^2}$
$x_{\text{next}}$ $=$ $\frac{2}{3}11+\frac{1331}{3\times {11}^2}$
$x_{\text{next}}$ $=10.999$ ....(1)
Assume $x=10.99$
$x_{\text{next}}=$ $\frac{2}{3}10.99+\frac{1331}{3\times {10.99}^2}$
$x_{\text{next}}=10.99$ ....(2)
Since we are getting $10.99$ in (1) and (2)
So, the approximate value of $\sqrt[3]{31333}$ $=10.99$