To begin, let’s understand what a square of a number means. When you multiply a number by itself, the result is called its square. For example, the square of 4 is 16 because 4 × 4 = 16. Similarly, the square of -3 is 9 since -3 × -3 = 9. No matter what number you square, the result is always positive.

Now, when we talk about "Square 1 to 30", we mean finding the squares of all numbers from 1 to 30. That means we calculate 1 × 1, 2 × 2, 3 × 3, and so on up to 30 × 30.

In short:

• A square number is written in exponent form as (x)².
• The smallest square in this list is (1)² = 1.
• The largest square in this list is (30)² = 900.

The chart given below shows the squares of numbers from 1 to 30.

Square 1 to 30 Table

The table given below shows the square values of numbers from 1 to 30:

Note: It is good for faster math calculations if we memorize these squares 1 to30.

Square 1 to 30 of Even Numbers

The table given below shows the square values of numbers from 1 to 30 for even numbers:

Square 1 to 30 of Odd Numbers

The table given below shows the square values of numbers from 

1 to 30 for odd numbers:

How to Calculate Values of Squares 1 to 30?

The square 1 to 30 can be found by the following methods which are given below:

• Multiplication by itself
• Using algebraic identities

Method 1: Multiplication by itself

In this method, the number is multiplied by itself, then the product gives us the square of that number. Let us understand this with the help of an example.

For example, the square of 16 = 16 × 16 = 256. Here, the resultant product “256” gives us the square of the number “16”.

This method is good for finding the square of smaller numbers.

Method 2: Using algebraic identities

In this method, we use basic algebraic identities to find the square of a number from 1 to 30. Let us understand this with the help of an example.

For example, find the square of 29.

We can express 29² as:

• 29² = (20 + 9)² = (20)² + 2 × (20) × (9) + (9)² = 400 + 360 + 81 = 841.
• 29² = (30 − 1)² = (30)² − 2 × (30) × (1) + (1)² = 900 − 60 + 1 = 841.

This method is good for finding the square of larger numbers.

Square 1 to 30 Solved Examples

Example 1:Two square wooden boards have sides of 8 meters and 6 meters. What is the total area of both boards?

Solution:
To find the area of a square, we multiply the side by itself (side × side).

• Area of the first board = 8 × 8 = 64 m²
• Area of the second board = 6 × 6 = 36 m²

So, the total area of both boards = 64 + 36 = 100 m².

The combined area of both wooden boards is 100 square meters.

Example 2: Find the sum of the first 30 odd numbers.

Solution: The sum of first n odd numbers is given as n².

⇒ Sum of first 30 odd numbers (n) = 30²

Using values from square 1 to 30 chart, the sum of the first 30 odd numbers = 30² = 900.

Example 3:Two square tiles have side lengths of 5 meters and 9 meters. What is the total area of both tiles?

Solution:
To find the area of a square, use the formula: Area = side × side

• Area of the first tile = 5 × 5 = 25 m²
• Area of the second tile = 9 × 9 = 81 m²

Now, add both areas: 25 + 81 = 106 m²

The total area of both tiles is 106 square meters.

We hope that the above article is helpful for your understanding and exam preparations. Stay tuned to the Testbook App for more updates on related topics from Mathematics, and various such subjects. Also, reach out to the test series available to examine your knowledge regarding several exams.