Cube

A number to the power of three is called the cube of the number

A cube is a number multiplied by itself three times. The cube of 2 is 8 (2 x 2 x 2)

How to Cube a Number easily and quickly

The cube of a number is that number multiplied by itself trice. For example, 5 cubed - denoted as 5³;is equal to 5×5×5 = 125. The technique for cubing any 2-digit number discussed below is based on the algebraic observation.

Step-1:

Write numbers in a row of 4 terms in such a way that the first one is the cube of the 1^st digit, second one is the square of 1^st number multiplied by 2^nd digit, third one is the 1^st digit multiplied by square of 2^nd digit and the fourth one is the cube of the 2^nd digit.

Step-2:

Write twice the values of 2nd and 3rd terms under the terms respectively in second row.

Step-3:

Add all the values column-wise and follow the carry over process.

Example: Find Cube of 14.

Step-1 : 1³ 1²×4 1×4² 4³

Worked-out row : 1 4 16 64

Step-2 : 8 32

Step-3 : Add the values column wise.

First Column from Right: Bring down 4 and carry over 6.

Second Column from Right: 16+32+6=54. Bring down 4 and carry over 5.

Third Column from Right: 4+8+5 = 17. Bring down 7 and carry over 1.

Fourth Column from Right: 1 + 1 = 2. Write down 2.

This 2,744 is the cube of the number 14.

Cubes of Some Natural Numbers

Some Interesting Patterns

1. Adding Consecutive Odd Numbers

This shows that if we add the consecutive odd numbers then we get the cube of the next number.

2. Cubes and their Prime Factors

Prime factorization of a number is done by finding the prime factors of the number and then pairing it in the group of three. If all the prime factors are in the pair of three then the number is a perfect cube.

Example

Calculate the cube root of 13824 by using prime factorization method.

Solution

First of all write the prime factors of the given number then pair them in the group of three.

Since all the factors are in the pair of three the number 13824 is a perfect cube.

Smallest Multiple that is a Perfect Cube

As we have seen that the group of three prime factors makes a number perfect cube, so to make a number perfect cube we need to multiply it with the smallest multiple of that number.

Example

Check whether 1188 is a perfect cube or not. If not then which smallest natural number should be multiplied to 1188 to make it a perfect cube?

Solution

1188 = 2 × 2 × 3 × 3 × 3 × 11

This shows that the prime numbers 2 and 11 are not in the groups of three. So, 1188 is not a perfect cube

To make it a perfect cube we need to multiply it with 2 × 11 × 11 = 242, so, it will make the pair of 2, 3 and 11.

Hence the smallest natural number by which 1188 should be multiplied to make it a perfect cube is 242.

And the resulting perfect cube is 1188 × 242 = 287496 ( = 66³).

Find Cube Of any Number

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