Question

Given that 4913 is a perfect cube. Estimate its cube root without factorisation?

Answer 1

By grouping the digits, we get 4 and 913
We know that, since, the unit digit of cube is 3, the unit digit of cube root is 7.
∴ we get 7 as unit digit of the cube root of 4913.
We know 1³ = 1 and 2³ = 8.
1 > 4 > 8.
Thus, 1 is taken as tenth digit of cube root.
$\sqrt[3]{34913}$= 17.