We will learn the short-cut method for finding the cube of a two-digit number.

Suppose, we have (a + b)³ = a³ + 3a²b + 3ab² + b³.

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;

**1. Find the value of (29)³ by the short-cut method.
Solution: **

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:**

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

● **Cube and Cube Roots**

**To Find if the Given Number is a Perfect Cube**

**Method for Finding the Cube of a Two-Digit Number**

● **Cube and Cube Roots - Worksheets**

**Worksheet on Cube and Cube Root**

**8th Grade Math Practice** **From Method for Finding the Cube of a Two-Digit Number to HOME PAGE**

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