Question

Making use of the cube root table, find the cube root
7532 . 

Answer 1

We have: \[7500 < 7532 < 7600 \Rightarrow \sqrt[3]{7500} < \sqrt[3]{7532} < \sqrt[3]{7600}\]

From the cube root table, we have: 

\[\sqrt[3]{7500} = 19 . 57 \text{ and } \sqrt[3]{7600} = 19 . 66\]

For the difference (7600 - 7500), i.e., 100, the difference in values

\[= 19 . 66 - 19 . 57 = 0 . 09\]

  For the difference of (7532 - 7500), i.e., 32, the difference in values

\[= \frac{0 . 09}{100} \times 32 = 0 . 0288 = 0 . 029\]  (up to three decimal places)

∴  \[\sqrt[3]{7532} = 19 . 57 + 0 . 029 = 19 . 599\]