So you know the last digit of the cube root of a number.
Q.
Do you want to know:
a) How many digits will be in the cube root?
b) What is the first digit of a cube root as well?
c) What is the last digit of the cube root?
Sol.
a) Divide the given number into 3-digit groups. If you are left with a single digit or a double digit
group, consider it also as one such group. Count the number of the groups. This is equal to the number
of digits in the cube root.
Ex: How many digits are there in ?
Dividing the number into 3-digit groups from the right and numbering them as shown.
We have four groups.
∴ There will be four digits in the cube root.
b) The first digit of the cube root is obvious from the first group of the number. In the example
above, the first group is 73.
Intuitively 33 = 27, 43 = 64, 53 = 125 which is
exceeding 73.
So, 4 is the first digit.
c) Since the number is ending with 8, from the table above, we know that the cube root ends in '2' (or
complement of 8 from 10 is 2).
So we know the first digit, last digit and the number of digits in any perfect cube root!