Over the last few weeks we have discussed different methods of finding the squares of numbers. Now let us look at easy methods to find the cube of two-digit numbers. As with squares, a prerequisite is to be thorough with the cubes of the one-digit numbers. The cubes of numbers 1-10 is given below:
The next thing to remember is a formula:
(a+b)3 = a3 + 3a2b + 3ab2 + b3
Writing this formula in a different way, we can find the cube of any two-digit number easily. The formula can be depicted as follows for easy calculation.
In the above table, we have split the 3a2b into a2b and 2a2b, and 3ab2 into ab2 and 2ab2. Then we add vertically to put down the final answer.
Example: Find 323
We have a = 3, b = 2
a3 = 27
a2b = (32 x2) = 18
ab2 = (3 x 22) = 12
b3 = 8
Then we can put the numbers as follows:
Answer: 32768
The base being 10, we put only the units digits down and carry over the higher digits.
Example: 453
a = 4, b = 5, so our problem will be like this,
Answer: 91125
In the final step we need to be careful putting down the digits. In every place we retain only the units digit and carry over the rest. The only thing to be cautious about is putting the right digits in place, which needs practice, and then the calculation is very easy.
Now you can try 343, 513, 223.