Question

Making use of the cube root table, find the cube root
7342 .

Answer 1

We have: \[7300 < 7342 < 7400 \Rightarrow \sqrt[3]{7000} < \sqrt[3]{7342} < \sqrt[3]{7400}\]

From the cube root table, we have: 

\[\sqrt[3]{7300} = 19 . 39 \text{ and }  \sqrt[3]{7400} = 19 . 48\]

For the difference (7400 - 7300), i.e., 100, the difference in values

\[= 19 . 48 - 19 . 39 = 0 . 09\]

∴  For the difference of (7342 - 7300), i.e., 42, the difference in the values

 

\[= \frac{0 . 09}{100} \times 42 = 0 . 0378 = 0 . 037\]

∴ \[\sqrt[3]{7342} = 19 . 39 + 0 . 037 = 19 . 427\]