Last week we discussed cubes, this week let us go one step further and discuss cube roots. Just like in squares, it is first important to know the cubes table for numbers 1 to 10. If we know this we can calculate the cube root of the perfect cube number mentally just by looking at the number. So let us first get familiar with the cube of the first ten numbers from the table below:

We can deduce the following points from this:

- The units digit of any cube is unique.
- The cube of 1 is 1 and that of 11 is 1331. So any number with 1 as the

units digit will have 1 as the units digit in its cube.

- Numbers with 4, 5, 6, 9 and 0 in the units place will have the same

number in the units place in the cube.

- The cube of 2 has 8 and the cube of 8 has 2 in the units place.
- The cube of 3 has 7 and the cube of 7 has 3 in the units place.
- The cube of any number ending with zero has a minimum of 3 zeros in its final digits.

One special fact about a cube is that the digit sum of a perfect cube will be 1, 8 or 9. This fact can be used to check whether a number is a perfect cube or not.

Let us check whether the following numbers are perfect cubes or not.

Consider 79507

- First let us find the sum of the digits. 7 + 9 + 5 + 0 + 7 = 28 = 2 +8 = 1. So it may be a perfect cube.
- It ends with 7, so the cube root will end with 3.

Consider 17562

- The sum of the digits is 1 + 7 + 5 + 6 + 2 = 21 = 3. So we know it is not a perfect cube.

What will be in the unit’s digit of the cube of 36?

- Answer: 6, because we know that a number that ends with 6 will have a cube that ends with 6.

What can you say about the units digit of the cube of 87?

- Its units digit is 7 so the cube will have 3 as the units digit.

Now check which of these may be a perfect cube?

456533

42876

238328

157466

Tip of the week: Understanding concepts will helps us to solve any problem.