Question

Is the long division method used for finding the cube roots?

Answer 1

Long divising method can be used to find the cube root, but it is very complex process.
The best way is to use prime factorization method
or, for perfect can be number you can use the short - cut as factors -
Eg - 12167
1. Split it in groups of 3 $\underset{–}{12}\underset{–}{167}$
2. The unit digit of its cube root will be 3.
as $3\times 3\times 3=27$
3. Now, consider next group (12)
$12<3^3\&12>2^3\Rightarrow 2^3<12<3^3$
$\therefore$ Choose 2.
$\therefore$ Cube root is 23.