Square of 1 to 30

The square of a number means multiplying the given number ‘x’ with itself. For example, x² = x × x. Square numbers are very good for solving various mathematical calculations, which helps in mathematical study. The square of a number from 1 to 30 will come in between from 1 to 900.

In exponential form, the square is written as x², indicating that the square of a number is calculated by multiplying x by itself. The smallest value of x is 1, so 1 × 1 = 1. The largest value occurs when x is 30, so 30 x 30 = 900. So, the squares of numbers from 1 to 30 comes between from 1 to 900.

The squares of the numbers are mainly used in mathematics, geometry, construction, and many other areas. The chart below helps us to understand the square of the number more clearly.

The square of a number is obtained as a result of multiplication of that number by itself. Here, the list of square numbers between 1 and 30.

Square of 1 to 30 - Even Numbers

An even number is a number that is evenly divisible by 2 without any remainder. The even numbers from 1 to 30 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30. Learning the squares of these numbers is also important. Here, the table below shows the square of the even numbers from 1 to 30.

Square of 1 to 30 - Odd Numbers  

An odd number is a number that cannot evenly divisible by 2 with remainder. The odd numbers from 1 to 30 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29. Learning the squares of these numbers is also important. The following table tells square of odd numbers from 1 to 30.
 

The squares of numbers from 1 to 30 can be easily calculated using two different methods:

• Multiplication Method
   
• Expansion Method

This method includes the multiplication of the number by itself two times to find its square. Use these steps to determine the square of a number:

Step 1: First write the number which we need to multiply. For example, 2

Step 2: Multiply 2 by itself to get 22. For example, 2 x 2 = 4

This method includes the algebraic expressions to expand and also for finding the square of a number. Use these steps to determine the square of a number:

Step 1: First write the number. For example, 22

Step 2: Break the number according to the place value. For example, 22 = 20 + 2

Step 3: Applying Formula - (a + b)² = a² + 2ab + b²
For example, (20 + 2)² = 20² + 2 (20)(2) + 2²

Step 4: Therefore, 222 = 400 + 80 + 4 = 484

For writing the square of a number, there are specific rules. Now, let's explore the rules for square numbers from 1 to 30.

Rule 1: Multiplication Rule

It means multiplication of the number by itself two times to find its square. For example, 25²  = 25 × 25 = 625.

Rule 2: Addition for Progressive Squares

This method calculates square numbers by adding consecutive odd numbers. For example, to calculate 3², first take 1² = 1, 2² = 1 + 3 = 4, 3² = 1 + 3 + 5 = 9.  

Rule 3: Estimation for Large Numbers

To find it for larger numbers, first break the numbers based on place value. Then, apply the correct formula (a - b)² = a² - 2ab + b² to calculate the result. For example, 29² = (30 - 1)² = 30² - 2 (30) (1) + (1)² = 900 - 60 + 1 = 841.

Students can easily learn the square of a number using following tips and tricks.

• The square of an even number is always even.

• The sum of successive even numbers can be used to describe a perfect square number.

• The square of any negative number will be positive.

• Perfect Square: The product of the number when multiplied by itself, which is always a whole number, is a perfect square. For example, 4² = 16, so 16 is the perfect square. 

• Even Numbers: A square number that we get from squaring an even number. For example, 2, 4, 6, 8 and so on.

• Odd Numbers: A square number that we will get from squaring an odd number. For example, 1, 3, 5, 7, 9 and so on.

• Progressive Squares: The method calculates square numbers by adding odd numbers. For example, 1 + 3 = 4, 1 + 3 + 5 = 9.