Squares and Cubes

Square of a Number

The square of a number is the multiplication by itself. That means, for any integer, we can obtain the square by multiplying the integer itself. For example, the square of an integer 4 will be: 4 × 4 = 16, i.e., the square of 4 is equal to 16.

This can be written using exponent as: 4² = 4 × 6 = 16

In the same way, we can find the squares of numbers or square numbers.

Thus, the notation for writing the square of a number “n” is n².

Cube of a Number

The cube of a number is the multiplication by itself thrice. That means, for any integer, we can obtain the cube by multiplying the integer by its square. For example, the cube of an integer 5 will be: 5² × 5 or 5 × 5 × 5, i.e., the cube of 5 is equal to 125.

This can be written using exponent as: 5³ = 5 × 5 × 5 = 125

In the same way, we can find the cubes of given numbers and the values obtained here are called perfect cube numbers.

Therefore, we can give the notation for writing the square of a number “n” as n³.

Squares and Cubes table

The list of squares and cubes upto 50 is given in the table below.

The above contains squares and cubes of numbers from 1 to 50. These are very useful for the students who are preparing for competitive exams. Memorising these values will help in managing the time while performing numerical calculations.

Chart of Squares and Cubes

The square and cubes of 1 to 20 are given in the below chart.

Squares and Cubes PDF

Get the pdf of the square, cubes, square root and cube root of numbers here.

Click here to download the PDF of Squares and Cubes of numbers:- Download PDF

Squares and Cubes upto 30

The below table shows the squares and cubes from 1 to 30 along with their notations. These values will help the students in solving numerical problems quickly.

Solved Examples 

Example 1:

Evaluate: 9³ – 19²

Solution:

Cube of 9 = 9³ = 9 × 9 × 9 = 729

Square of 19² = 19 × 19 = 361

Now, 9³ – 19² = 729 – 361 = 368

Example 2:

If b² = 2209, find the value of b.

Solution:

Given, b² = 2209

As we know, the square of 47 is 2209.

That means 47² = 47 × 47 = 2209

Therefore, b = 47.

Example 3:

A cube has an edge of 8 units. Find the volume of the cube.

Solution:

Given,

Edge of a cube = a = 8 units

Volume of the cube = a³

= 8³

= 8 × 8 × 8

= 512 cubic units

Therefore, the volume of the cube is 512 cubic units.

Practice Problems

1. Find the area of a square field whose side length is 23 m.
2. Calculate the value of 12² + 13³.
3. What is the sum of cubes of the first 5 natural numbers?

Recommended Videos

How to Find the Square of a Number?

How to Find Cube and Cube Roots of Numbers?

For more maths related articles, visit byjus.com and download BYJU’S – The Learning App for interactive videos on mathematical concepts.