Chapter

This chapter has two methods of cubing. 

• Method 1: Cubing by the ratio method
• Method 2: Cubing by general formula

Before proceeding to the methods the student should memorize the cubes of first 10 natural numbers stated below.

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

7³ = 343

8³ = 512

9³ = 729

10³ = 1000

Method 1: Cubing by the ratio method

Example 1 :   12³

Step 1:  Make 4 boxes. Write the cube of left digit in  the left box  1³  = 1

Step 2: Calculate the ratio of right to left digit ratio r = R/L = 2/1 = 2

Step 3: Multiply the number in left box by this ratio r and keep on subsequently multiplying the numbers obtained in the boxes, by same ratio till you reach the last (IV^th) box

Step 4: Double the numbers in the second and third box and write below them

Step 5: Add up the numbers box wise from right to left and carry over wherever required to obtain the final answer as 1728  

Example 2 :

Example 3 : 

Example 4 : 

Example 5 :

Exercises:

15³  = 15625

27³  = 19683

22³  = 10648

35³  = 42875

51³  = 132651

65³  = 166375

13³  = 2197

16³  = 4096

19³  = 6859

97³  = 912673

99³  = 970299

Method 2:  Cubing by using general formula

Example 1 :

          (Note the carry over from the right boxes to the left boxes)

Example 2 :

Example 3 :

Exercises:

11³  = 1331

17³  = 4913

18³  = 5832

26³  = 17576

25³  = 15625

37³  = 50653

42³  = 74088

52³  = 140608

63³  = 250047

75³  = 421875

81³  = 531441

98³  = 941192

Corollary:

We can extend the general formula to calculate the cube of three digit numbers as well.

Example 1:  105³  (Here we need to substitute a = 10 and b = 5 in the above formula).

Example 2:  103³ 

Example 3:  102³