Question

Fill in the blanks to make the statement true.
There are _______________ perfect cubes between 1 and 1000

Answer 1

Hint: To fill the given blank we will find the perfect cube of each natural number till we get a cube which is greater than 1000. Firstly we will start by 1 and find its cube by multiplying the number three times by itself. We will keep this process till we get the cube which is equal to or greater than 1000 and get the desired answer.

Complete step by step answer:
We have to find the perfect cube between 1 and 1000.
So let us form a table for each natural number multiplied three times by it-self as follows:

Number	Cube
1	$1\times 1\times 1=1$
2	$2\times 2\times 2=8$
3	$3\times 3\times 3=27$
4	$4\times 4\times 4=64$
5	$5\times 5\times 5=125$
6	$6\times 6\times 6=216$
7	$7\times 7\times 7=343$
8	$8\times 8\times 8=512$
9	$9\times 9\times 9=729$
10	$10\times 10\times 10=1000$

Now as we can see we got the cube as 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000.
 We have to find a perfect cube between 1 and 1000 so there are 8 perfect cubes between them which are 8, 27, 64, 125, 216, 343, 512 and 729.
Hence there are 8 perfect cubes between 1 and 1000

Note: When a number is multiplied three times by itself the product is known as the cube of that number. A perfect cube is the one which is a cube of a natural number that is when we find the cube root of that value we get a natural number. Or we can say that a given natural number is a perfect cube if it can be expressed as the product of triplets of equal factors.