Question

Making use of the cube root table, find the cube root
34.2 .

Answer 1

The number 34.2 could be written as \[\frac{342}{10}\]

Now

\[\sqrt[3]{34 . 2} = \sqrt[3]{\frac{342}{10}} = \frac{\sqrt[3]{342}}{\sqrt[3]{10}}\]

Also

\[340 < 342 < 350 \Rightarrow \sqrt[3]{340} < \sqrt[3]{342} < \sqrt[3]{350}\]

From the cube root table, we have:  \[\sqrt[3]{340} = 6 . 980 and \sqrt[3]{350} = 7 . 047\]

For the difference (350 - 340), i.e., 10, the difference in values

\[= 7 . 047 - 6 . 980 = 0 . 067\] .

∴  For the difference (342 -340), i.e., 2, the difference in values

\[= \frac{0 . 067}{10} \times 2 = 0 . 013\]   (upto three decimal places)

∴ \[\sqrt[3]{342} = 6 . 980 + 0 . 0134 = 6 . 993\]  (upto three decimal places)

  From the cube root table, we also have: \[\sqrt[3]{10} = 2 . 154\]

∴ \[\sqrt[3]{34 . 2} = \frac{\sqrt[3]{342}}{\sqrt[3]{10}} = \frac{6 . 993}{2 . 154} = 3 . 246\]

Thus, the required cube root is 3.246.