# Perfect Cubes: The Key to Unlocking Complex Mathematical Problems

## What are Perfect Cubes?

A number can be defined as a perfect cube by multiplying it by itself three times.

If a is a perfect cube of b then, a = c

Example: 27 is a perfect cube, then

27 = 33

∛27= 3

This unique sign denotes “cube root” and is denoted by a little three = This unique sign denotes “cube root” and is denoted by a little three = ∛

A cube is essentially a square with three dimensions. Each side is the same length. 12 sides make a cube. It is composed of six squares, referred to as faces.

## Perfect Cube Roots 1 to 50

There are a total number of 10 cubes between 1 to 1000 which are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000.

## Perfect Cubes Between 1 to 100

There are a total number of 4 cubes between 1 to 100 which are 1, 8, 27 and 64.

## Perfect Cubes Between 101 to 200

There is only one cube between 101 to 200 which is 125.

## Perfect Cubes Between 201 to 300

There is only one cube between 201 to 300 which is 216.

## Perfect Cubes Between 301 to 400

There is only one cube between 301 to 400 which is 343.

## Perfect Cubes Between 401 to 500

There are no cubes between 401 and 500.

## Perfect Cubes Between 501 to 600

There is only one cube between 501 to 600 which is 512.

## Perfect Cubes Between 601 to 700

There are no cubes between 601 and 700.

## Perfect Cubes Between 701 to 800

There is only one cube between 701 to 800 which is 729

## Perfect Cubes Between 801 to 900

There are no cubes between 801 and 900.

## Perfect Cubes Between 901 to 1000

There is only one cube between 901 to 1000 which is 1000.

## Understanding the Properties of Perfect Cube Numbers

Properties of Perfect Cube Numbers

1. All even natural number cubes are also even in nature.

2. All odd-number cubes are odd in nature.

3. The sum of the cubes of first natural numbers(n) is equal to the square of their sum.

(1+2+3+……+𝑛)²

4. The numerals ending in the same digit are known as cubes of the numbers 4, 5, 6, and 9.

Numbers that end in the digit 2 have cubes that end in the digit 8.

Numbers that end in the digit 8 have cubes that end in the digit 2.

Numbers that end in the digit 3 and 7 have cubes that end in the digits 7 and 3 respectively.

5. If a prime number p divides m, then p × p × p will divide m × m × m, i.e., p3 will divide m3.

Thus, if a prime number p divides a perfect cube, then p3 also divides this perfect cube.

## How to Find Cube Numbers?

When a number is multiplied by itself three times, the result is referred to as the cube of that number.

Here are several simple ways to calculate a number’s cube without a calculator.

Firstly, recall the cubes of the numbers between 1 and 10.

## How to Find Cube Numbers?

### 1. Simple Multiplication

Here you calculate the cube of a number by simply multiplying a number, like old school.

Example: Find the cube of 56

Multiply 56 x 56

now again multiply this by 56; 3136 x 56

### 2. Cube of a Number that Ends with Zero

Example: Find the cube of 80

remember the cube of 8?

83 = 512,

now add three zeros on the right side

803 = 512000

### 3. Cube of a Number Just Near to Ten Place

Example: Find the cube of 11

Use the simple algebra formula  (a + b)³ = a³ + 3a²b + 3ab² + b³

we can write 113  = ( 10 + 1 )3

so here take a = 10 , b = 1 then

( 10 + 1 )3

= 1000 + 300 + 30 + 1

= 1331.

## How to Find the Cube Root of a Non-Perfect Cube?

Many numbers are not ideal cubes, which are also known as non-perfect cubes, so we cannot use the prime factorization and estimation approach to determine the cube root of these numbers.

Example 1: Let’s take out the cube root of 100.

Now we know that 100 is not a perfect cube because it lies between 64 and 125, that is cube roots of 4 and 5.

3√100

=4.64158883361

Example 2: Let’s take out the cube root of 555.

Now we know that 100 is not a perfect cube because it lies between 512 and 729, that is cube roots of 8 and 9.

3√555

=8.21796576488

## Understanding the Applications of Perfect Cube Roots in Everyday Life

Numerous common tasks need the use of square roots and cube roots.

They are employed in technology, flooring, architecture, engineering, and carpentry. The Pythagorean theorem is applied in numerous circumstances in real life, including:

1. Painting on the Wall

Consider a painter who needs to cover a wall that is roughly 3 metres high. To prevent it from tipping, he must position the ladder’s base 2 metres away from the wall. What kind of ladder will the painter need to finish his job, and how long will it be? You may determine that he requires a ladder that is roughly 3.6 metres high using Pythagoras’ theorem.

2. Choosing the Appropriate Things

If you need a PC that can accommodate a 22-inch display for your workstation. A 16″ by 10″ monitor was in your possession. Can the computer be accommodated in your cabin? You may determine this using Pythagoras’ Theorem.

## FAQ's on Perfect Cubes

The square root of 4 is represented by the expression √4, where ‘√’ is the square root symbol. Thus, 4 a perfect root.

No, 32 is not a perfect root; the square root of the number 32 is a non-terminating, irrational number.

50, 75 and 99 are not perfect cubes.

## Conclusion: Start Exploring the World of Perfect Cubes Today!

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