Question

How many perfect cube numbers are present between 1 and 1001.

Answer 1

Hint:
In order to find the number of perfect cube numbers between 1 and 1001 we find the nearest cube number of 1 and the nearest cube number of 1001, from which we can find the number of perfect cube numbers.

Complete step by step solution:
We are given two numbers 1 and 1001.
We are asked to find the number of perfect cube numbers between them. We know that 1 is a perfect cube number.
$ \Rightarrow {1^3} = 1$
Then the nearest cube number of 1001 is 1000 as
$ \Rightarrow {10^3} = 1000$
Hence we can see that the cube numbers between 1 and 1001
$ \Rightarrow {2^3}, {3^3}, {4^3}, {5^3}, {6^3}, {7^3}, {8^3}, {9^3}, {10^3}$

From this we can see that the number of perfect cube numbers between 1 and 1001 is 9.

Additional information :
1) Numbers obtained when a number is multiplied by itself three times are known as cube numbers.
2) Cube of odd number is odd; Cube of even number is even.
3) If in the prime factorisation of any number each factor appears three times, then the number is a perfect cube.

Note:
1) Many students tend to leave out 1000 or add 1 while counting the number of perfect cubes but we are just asked the number of cubes in between 1 and 1001 hence we leave out 1 .