Question

Making use of the cube root table, find the cube root
8.65 .

Answer 1

The number 8.65 could be written as\[\frac{865}{100}\] .

Now

\[\sqrt[3]{8 . 65} = \sqrt[3]{\frac{865}{100}} = \frac{\sqrt[3]{865}}{\sqrt[3]{100}}\]

Also

\[860 < 865 < 870 \Rightarrow \sqrt[3]{860} < \sqrt[3]{865} < \sqrt[3]{870}\]

From the cube root table, we have: 

\[\sqrt[3]{860} = 9 . 510 \text{ a nd }  \sqrt[3]{870} = 9 . 546\]

For the difference (870 - 860), i.e., 10, the difference in values \[= 9 . 546 - 9 . 510 = 0 . 036\]

∴  For the difference of (865- 860), i.e., 5, the difference in values

 

\[= \frac{0 . 036}{10} \times 5 = 0 . 018\]   (upto three decimal places)

∴ \[\sqrt[3]{865} = 9 . 510 + 0 . 018 = 9 . 528\]  (upto three decimal places)

From the cube root table, we also have: \[\sqrt[3]{100} = 4 . 642\]

∴ \[\sqrt[3]{8 . 65} = \frac{\sqrt[3]{865}}{\sqrt[3]{100}} = \frac{9 . 528}{4 . 642} = 2 . 053\]  (upto three decimal places)

Thus, the required cube root is 2.053.