VALUES OF CUBES OF NUMBERS FROM 1 TO 30

When a number is raised to the power 3, it is called the cube of a number. We cannot memorise the cube of every number. It is good if we learn the cubes of some numbers. In this article, we are going to discuss the values of cubes from 1 to 30.

Values of cubes from 1 to 30

How to find the cube of the number?

To find the cube of a number, we can multiply it three times by itself.

For eg- 8^3=8\times 8\times 8=512.

We can also find the cube with the help of the following expression –

(p+q)^3=p^3+q^3+3pq(p+q) \text{ or } (p-q)^3=p^3-q^3-3pq(p-q)

We can write 8 as (6 + 2), here- p = 6, q = 2

Using the first expression, 

(6+2)^3=6^3+2^3+3\times 6\times 2(6+2)

                 = 216 + 8 + 36 × 8  

                 = 224 + 288

                 = 512

We can also write 8 as (10 – 2) where p = 10 & q = 2.

Using the second expression,

(10-2)^3=10^3-2^3-3\times 10\times 2(10-2)

                   = 1000 – 8 – 60 × 8

                   = 1000 – 8 – 480

                   = 512

Solved Questions

Q1. What is the value of 7^3+8^3+9^3?

Solution:

We know the cube of 7, 8 and 9 are 343, 512 and 729 respectively.

So, the value is:

7^3+8^3+9^3=343+512+729=1584

Q2. Subtract three times the cube of 19 from 2 times the cube of 25.

Solution:

We need to subtract 3\times 19^3 \text{ from }2\times 25^3.

25^3=15625\text{ and } 19^3=6859

\therefore 2\times 25^3- 3\times 19^3=2\times 15625-3\times 6589

                                         = 31250 – 20577 

                                         = 10673

Q3. By what number should we multiply the cube of 2 to get the cube of 4?

Solution:

We know that, 2^3=8\text{ and }4^3=64

Let the number to be found is ‘x’.

8x = 64

 x = 8

Hence cube of 2 should be multiplied by 8(i.e., cube of 2 itself) to get the cube of 4.