Answer
Verified
378k+ views
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:
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.
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE