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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}$
$=1.260 \times 8.763$
$=11.04138$
$=11.041$