Answer:

Step-by-step explanation:

METHOD:

For finding the cube of a two-digit NUMBER with the tens digit = a  

and the units digit = b, we make four columns, headed by  

a³, (3a² × b), (3a × b²) and b³  

The rest of the PROCEDURE is the same as followed in squaring a number by the column method. We simplify the working as;  

a² × a = a³;  

a² × 3b = 3a²b;  

b² × 3a = 3ab²;  

b² × b = b³;

Examples on the method for finding the cube of a two-digit number:

1. Find the VALUE of (29)³ by the short-cut method.

SOLUTION:  

Method for Finding the Cube of a Two-Digit Number

Here, a = 2 and b =9.

a² × a = a³;

a² × 3b = 3a² × b;

b² × 3a = 3a × b²;

b² × b = b³  

Therefore, (29)³ = 24389  

2. Find the value of (71)³ by the short-cut method.  

Solution:

Method for Finding the Cube of a Two-Digit Number

Here, a = 7 and b = 1

a² × a = a³;  

a² × 3b = 3a² × b;  

b² × 3a = 3a × b²;  

b² × b = b³

Therefore, (71)³ = 357911  

By following the above examples on the method for finding the cube of a two-digit number; we can try to find the value of each of the following using the short-cut method;

1. (25)³  

2. (47)³

3. (68)³

4. (84)³