Example of perfect cube and non perfect cube of a numbers are respectively

What are Perfect Cubes?

Perfect cubes are the numbers that are the triple product of the same number. In other words, a perfect cube is a value that is the result of three times multiplication of a whole number to itself. A perfect cube is a number, that can be written as three times the product of the same number.

The cube root of a perfect cube always results in a whole number. But we can find cubes of any number whether it is an integer or a fraction. For example, the cube of 0.5 is:

0.5 × 0.5 × 0.5 = 0.125

Let us see the list of perfect cubes in the next section.

List of Perfect Cubes 1 to 50

Number (x)Multiplied Three times by itselfCubes (x3)11× 1× 1122× 2× 2833× 3× 32744× 4× 46455× 5× 512566× 6× 621677× 7× 734388× 8× 851299× 9× 97291010× 10× 1010001111× 11× 1113311212× 12× 1217281313× 13× 1321971414× 14× 1427441515× 15× 1533751616× 16× 1640961717× 17× 1749131818× 18× 1858321919× 19× 1968592020× 20× 2080002121× 21× 2192612222× 22× 22106482323× 23× 23121672424× 24× 24138242525× 25× 25156252626× 26× 26175762727× 27× 27196832828× 28× 28219522929× 29× 29243893030× 30× 30270003131× 31× 31297913232× 32× 32327683333× 33× 33359373434× 34× 34393043535× 35× 35428753636× 36× 36466563737× 37× 37506533838× 38× 38548723939× 39× 39593194040× 40× 40640004141× 41× 41689214242× 42× 42740884343× 43× 43795074444× 44× 44851844545× 45× 45911254646× 46× 46973364747× 47× 471038234848× 48× 481105924949× 49× 491176495050× 50× 50125000

How to Find a Perfect Cube?

Every number can be expressed as the product of the power of its Prime factors. If the power of all the Prime factors is in the multiple of 3, then the number is said to be a perfect cube.

1) 15 = 3 × 5

153 = 15 × 15 × 15 = 3 × 5 × 3 × 5 × 3 × 5 = 33 × 53

2) 18 = 2 × 3 × 3

183 = 18 × 18 × 18 = 2 × 3 × 3 × 2 × 3 × 3 × 2 × 3 × 3 = 23 × 33 × 33

From the above examples, we can observe that each prime factor of a number appears three times in the prime factorization of its cube.

Related Articles

• Cube
• Cubes From 1 to 50
• Cube Root 1 to 30
• Squares upto 50
• How to Find Cube Root
• Cube Roots of Unity
• Perfect Numbers

Solved Examples on Perfect Cubes

Question 1: Is the number 600 a perfect cube?

Let us write down, stating the prime factors of the number 600.

\(\begin{array}{l}600 = 2 \times 2\times 2 \times 3 \times 5 \times 5 = 2^{3}.3.5^{2} \end{array} \)

The number 600 is not a perfect cube as all the prime factors is not a multiple of three.

Question 2: What should be multiplied to the number 120 to make it a perfect cube?

\(\begin{array}{l} Factors\ of\ 120 = 2 \times 2 \times 2 \times 3 \times 5  = 2^{3}. 3.5\end{array} \)

The factor 2 occurs thrice, 3 and 5 occurs only once. So in order to make it a perfect cube we have to multiply 120 with a square of 3 and 5.

Therefore, 120 × 3 × 3 × 5 × 5 =27000

The number 27000 is the required perfect cube.

Application of Perfect Cubes

A cube is a three-dimensional figure which has all the edges of equal length. The volume of a cube is given by the product of its dimensions. For example, for a cube of edge length ‘a’ units, the volume of the cube is given by “a × a × a”which is equal to a3 cubic unit. Similarly, we can calculate the perfect cube of various numbers.

Illustration: Determine the volume of a cube with an edge length of 7 cm.

Solution: The side of the cube is 7 cm.

Volume = side × side × side = 7 × 7 × 7 = 343 cm3.

The numbers such as 1, 8, 27, 64, etc. are known as perfect cubes or cube numbers.

When a cube is broken or cut, total volume still remains the same. Hence, we can observe that to construct a cube of edge length ‘2a’ with cubes of edge length ‘a’ we need to have 8 cubes of edge length a.

This article explains perfect cubes and the method of their calculation. To learn more about other topics download BYJU’S – The Learning App and watch interactive videos. Also, take free tests to practice for exams.

Frequently Asked Questions on Perfect Cubes

What is a perfect cube?

When a natural number is multiplied three times to itself, then the resulting value is called perfect cube.

The opposite of cubing a number is finding the cube root. Since 53 = 125, the cube root of 125 is 5. The cube root of a perfect cube is an integer.

It is possible to get the cube root of a negative number. For example, the cube root of −125 is −5 since (−5) × (−5) × (−5) = −125.

The following table shows perfect cubes from 1 to 1000 and their corresponding cube roots. Scroll down the page for more examples of how to evaluate cube root of perfect cubes.

Perfect Cubes & Cube Roots

Evaluate Square Roots Of Perfect Squares And Cube Roots Of Perfect Cubes

How To Simplify Radicals With Negative Radicands And Odd Indexes?

To cube a number, we use the number in a multiplication 3 times.
For example, 4 cubed = 43 = 4 × 4 × 4 = 64

A cube root goes the other direction.
3 cubed is 27, so the cube root of 27 is 3.

The cube root of a number is the value that when cubed gives the original number.
The cube root of 27 is 3 because when 3 is cubed you get 27.

∛ is the special symbol that means “cube root”. It is the radical symbol √ with a little three to mean cube root.
You can use it like this:
∛27 = 3.

Perfect cubes are cubes of whole numbers.

It is easy to work out the cube root of a perfect cube, but it is hard to work out other cube roots.

How To Find The Smallest Multiple Of Another Number That Is Also A Perfect Cube?

Example:
What is the smallest positive whole number that is a perfect cube and is a multiple of 24?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

What is an example of a perfect cube number?

The numbers such as 1, 8, 27, 64, etc. are known as perfect cubes or cube numbers. When a cube is broken or cut, total volume still remains the same.

What are the first 20 perfect cubes?

Cube Numbers from 1 to 100.

Is 1331 a perfect cube?

A perfect cube is a number which is the cube of an integer. Since the cube of 11 is 1331, therefore 1331 is a perfect cube number.

What are the first 5 perfect cube numbers?

The first few are 1, 8, 27, 64, 125, 216, 343, ... (OEIS A000578).