Volume of cube = 275 cm3 (Given)
Let side of cube = a cm
So,
= \(a^3 = 275\)
= \(a = \sqrt[3]{275}\)
We know that value of \(\sqrt[3]{275}\) will lie between \(\sqrt[3]{270}\) and \(\sqrt[3]{280.}\)
From cube root table we get,
= \(\sqrt[3]{270}\) = 6.463 and \(\sqrt[3]{280.}\) = 6.542
So by unitary method,
∵ For difference (280 – 270 = 10 ) difference in cube root values = 6.542 – 6.463 = 0.079
∴ For difference (275 – 270 = 5) difference in cube root values =
Hence, \(\sqrt[3]{275} = 6.463 + 0.04 = 6.503.\)
Thus the required cube root is = 6.503.