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
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