Making use of the cube root table, find the cubes root of the following (correct to three decimal places)
1346

Given: 

1346

To find: 

We have to find the cube root of the given number correct to three decimal places using cube root table.

Solution:

$1346=2 \times 673$

$\Rightarrow \sqrt[3]{1346}=\sqrt[3]{2} \times \sqrt[3]{673}$

$670<673<680$

$\Rightarrow \sqrt[3]{670}<\sqrt[3]{673}<\sqrt[3]{680}$

From the cube root table, we have,

$\sqrt[3]{670}=8.750$ 

$\sqrt[3]{680}=8.794$ For the difference $(680-670)=10$,

The difference in the values $=8.794-8.750$

$=0.044$

This implies,

For the difference of $(673-670)=3$,

The difference in the values $=\frac{0.044}{10} \times 3$

$=0.0132$

$=0.013$

Therefore,

$\sqrt[3]{673}=8.750+0.013$

$=8.763$

$ \sqrt[3]{1346}=\sqrt[3]{2} \times \sqrt[3]{673}$

$=1.260 \times 8.763$

$=11.04138$

$=11.041$