Question

Find cube root of 1331.

Answer 1

Hint: Numbers that are obtained when a number is multiplied by itself three times are known as cube numbers. If m = ${{n}^{3}}$ , then m is the cube of n, and n is the cube root of m. A number whose units' digit is 1 has a cube whose units' digit is also 1 (see Note below). If a number has an n number of zeros at its end then it's cube will have 3n number of zeros at its end. Observe that ${{10}^{3}}$ = 1000 and ${{20}^{3}}$ = 8000, therefore, the cube root of 1331 must be between 10 and 20, in fact very close to 10.

Complete step-by-step answer:
Since the number 1331 lies between ${{10}^{3}}$ = 1000 and ${{20}^{3}}$ = 8000, its cube root must be between 10 and 20.
Also, the units' digit of 1331 is 1, therefore, the units' digit of its cube root must be 1.
So, the cube root of 1331 will be 11, provided 1331 is a perfect cube.
We check that 11 × 11 = 121 and 121 × 11 = 1331.
Therefore, the cube root of 1331 is 11.

Note: Cube numbers are also known as perfect cubes. Cubes of the numbers with units' digit 1, 4, 5, 6 and 9 are the numbers ending in the same units' digit. A number whose units' digit is 2 has a cube whose units' digit is 8 and vice versa. A number whose units' digit is 3 has a cube whose units' digit is 7 and vice versa. Some other Properties of Cube Numbers:
If a number has n number of zeros at its end then it's cube will have 3n number of zeros at its end.
The cube of an even number is always even and the cube of an odd number is always odd.
When a perfect cube or cube number is prime factorized, its factors can be grouped into triplets; groups of 3 identical primes.