Question

Making use of the cube root table, find the cube root
833 .

Answer 1

We have: \[830 < 833 < 840 \Rightarrow \sqrt[3]{830} < \sqrt[3]{833} < \sqrt[3]{840}\]

From the cube root table, we have: \[\sqrt[3]{830} = 9 . 398 \text{ and  } \sqrt[3]{840} = 9 . 435\]

For the difference (840 - 830), i.e., 10, the difference in values
\[= 9 . 435 - 9 . 398 = 0 . 037\]

∴  For the difference (833 - 830), i.e., 3, the difference in values

\[= \frac{0 . 037}{10} \times 3 = 0 . 0111 = 0 . 011\]  (upto three decimal places)

∴  \[\sqrt[3]{833} = 9 . 398 + 0 . 011 = 9 . 409\] .