Question

The unit digit of the cube root of 1331 is$$$$
A.1$$$$
B.2$$$$
C.3$$$$
D.0 $$$$

Answer 1

Hint: We divide the given number 1331 into two groups with numbers 331 in the first group and 1 in the second group. We use the fact that if we multiply any of number with the digit 1 at a unit place three times with itself the digit that will occur in its cube will be 1 since and conclude the unit digit as 1. We find the ${10}^{\text{th}}$ digit taking the cube root of the number in the second group.$$$$

Complete step by step answer:
The cube root of $a$ is denoted as $a^{{\displaystyle \frac{1}{4}}}=\sqrt[3]{3}$ which asks for the number we have to multiply three times to get $a$.
We know that if we multiply any of number with the digit 1 at unit place three times with itself the digit that will occur in its cube will be 1 since $1\times 1\times 1=1$.$$$$

The given number is 1331. We are asked to find the unit digit of 1331. So we first divide 1331 into groups of numbers with the first group taking 3 digits at a time from the right hand side at once. $$$$

So we have the number in the groups as 331 in the first group and 1 in the second group.

We investigate the number at first group 1331. The unit digit of 331 will be the unit digit of the cube root of 1331 which is 1. So the correct option is A. We observe the first group and see that$1^3=1$. So the digit at ${10}^{\text{th}}$place will be 1. So we have the cube root as 11. $$$$
Note:
 We note that the number of groups made is equal to the number of digits in the cube root. There are 3 cube roots of a number and if one is a real number other two are complex numbers. We can alternatively find the cube root of 1331 with prime factorization that is $1331=11\times 11\times 11$.