Question

Making use of the cube root table, find the cube root
5112 .

Answer 1

By prime factorisation, we have: \[5112 = 2^3 \times 3^2 \times 71 \Rightarrow \sqrt[3]{5112} = 2 \times \sqrt[3]{9} \times \sqrt[3]{71}\]

By the cube root table, we have: \[\sqrt[3]{9} = 2 . 080 and \sqrt[3]{71} = 4 . 141\]

∴ \[\sqrt[3]{5112} = 2 \times \sqrt[3]{9} \times \sqrt[3]{71} = 2 \times 2 . 080 \times 4 . 141 = 17 . 227\] (upto three decimal places)

Thus, the required cube root is 17.227.