**Cubes Cube Roots**

Hello Readers

Today’s Topic is – **Cubes & Cube Roots (Perfect and Imperfect)**

First, we will discuss how to find out the Cubes of the numbers and then, we will discuss the Cube Roots.

__CUBES__

Before discussing the tricks to find out the cubes of the numbers it is advisable to learn the Cubes up to 15.

Here is the table showing the cubes from 1 to 15.

The only method to learn these Cubes is Revision. Make your habit to revise these Cubes once in a day (at least) till you memorize them all.

Now, we will discuss how to solve the Cube of the numbers up to 100(but as said above learn cubes up to 15 to apply these tricks easily).

Now, let’s start discussing the trick.

There are two methods for this.

**Method 1**

We all know;

This will be the basic formula that we will use to find out Cubes.

We will split the formula according to our need;

Now let’s understand this trick with the help of example:

**24^3 = ?**

**Step 1**

a=2 and b = 4

**Step 2**

- The numbers used in the formulas are always in the ratio of a:b

Here, a=2 and b=4

So, there ratio will be 2:4 i.e. = 1:2

Now, compare it with the numbers used in the formula :

8:16 = 1:2

16:32 = 1:2

32:64 = 1:2

__CUBE ROOTS__

Now, let’s learn how to find cube roots (Perfect or Imperfect) of the numbers. First, we will discuss Perfect Cube roots and then, Imperfect Cube Roots.

**Perfect Cube Roots**

The trick to find out Perfect Cube Roots is basically based on Unit Places of the Cubes of the numbers.

Let’s observe Unit Places of the Cubes of the Numbers (Perfect)

It is easy to remember the unit places of Cubes as compared to the Unit Places of the Sqaures.

AS we can see, the unit places of the cubes are same to the numbers, expect in the case of four numbers (2,3,8 and 7). But there is vice versa condition for these numbers which is explained below

Below is the table showing the unit places of the numbers:

After observing the positions of the unit places, let’s start understanding the Trick with the help of example:

**Example: Find the cube of the number:**

**Step 1**

**Step 2**

**So, the Answer is 86.**

Isn’t this trick is so simple.

Now, let’s move on Imperfect Cube Roots.

**Imperfect Cube Roots**

The trick to find out Imperfect Cube is quite similar to the trick to find out the Imperfect Square Roots.

Let’s take one example to understand this trick:

**Example:**

**Step 1**

**Step 2**

**Step 3**

The trick to find the Imperfect Cube Root is little bit tricky but you can make it easy daily practice and implementing it to your daily practice routine.

So Readers, with this we will finish this topic. The more you practice friends, the more you will feel comfortable while applying these tricks. We hope you have enjoyed learning.

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