Square 1 to 30: In the study of Mathematics, the square of a number refers to a number that is factorized by the same pair of numbers. For example, the square of 4 is 16. Here the factor of 16 is 4x4, then means that 16 represents the square of 4. In this article, you will learn more about the values of squares 1 to 30, the list and chart of squares of numbers from 1 to 30, methods to find out the square, and solved examples. 

1 to 30 Square  Values

The square of numbers from 1 to 30 covers the list of squares of all the numbers coming in the range of 1 to 30. The value of squares of numbers from 1 to 30 includes the range from 1 to 900. These values assist students to simplify long mathematical equations quickly and easily. The square 1 to 30 in the exponential form is written as . For example, the square of 8 is 8^2 means 64. So the value of the square of 8 is 64.

Square 1 to 30 Table

The square 1 to 30 chart helps you to easily learn the values of the square of numbers from 1 to 30. It makes the time-taking equations simpler. The value of the square of numbers ranging from 1 to 30 is listed below.

Square from 1 to 30 Table
1² = 12² = 4
3² = 94² = 16
5² = 256² = 36
7² = 498² = 64
9² = 8110² = 100
11² = 12112² = 144
13² = 16914² = 196
15² = 22516² = 256
17² = 28918² = 324
19² = 36120² = 400
21² = 44122² = 484
23² = 52924² = 576
25² = 62526² = 676
27² = 72928² = 784
29² = 84130² = 900

For maintaining quicker calculations, students are suggested to memorize the square value from 1 to 30 thoroughly. 

Square 1 to 30 for Even Number

The value of squares of even numbers ranging from 1 to 30 is given below in table form.

Square 1 to 30 for Even Number
2² = 418² = 324
4² = 1620² = 400
6² = 3622² = 484
8² = 6424² = 576
10² = 10026² = 676
12² = 14428² = 784
14² = 19630² = 900
16² = 256 

Square 1 to 30 for Odd Number

The value of squares of odd numbers ranging from 1 to 30 is given below in table form.

Square 1 to 30 for Odd Number
1² = 117² = 289
3² = 919² = 361
5² = 2521² = 441
7² = 4923² = 529
9² = 8125² = 625
11² = 12127² = 729
13² = 16929² = 841
15² = 225 

How to Calculate Square 1 to 30?

There are 2 methods mentioned below for calculating the values of squares of numbers ranging from 1 to 30. 

Method 1- Multiplication by itself

Under this method, the value of the square is solved by the multiplication of a given number by itself. For example, the value of square of 6 = 6 × 6 = 36. Here, the final product 36 tells that it is the square of the number 6. This method is generally applied to smaller numbers.

Method 2- Applying basic Algebraic Formulas

Under this method, a given number n is first written as (a+b) or (a-b), where ‘a’ is a multiple of 10 and ‘b' refers to any value less than 10. After that, the fundamental algebraic formula is applied to calculate the value of squares of the given number. In this method, the 2 basic algebraic identities formulas can be applied to find the value of squares of a number. (a + b)² = a² + b² + 2ab or (a - b)² = a² + b² - 2ab. This method is preferred where b has a smaller value. For example, for finding the square of 28, we can write it as (20+8) as option 1 or (30-2) as option 2.

Next, we need to apply the basic algebraic formula and then we have,

Option 1: [20² + 8² + (2 × 20 × 8)] or Option 2: [30² + 2² - (2 × 30 × 2)] 

After expanding the expressions further, 

we get Option 1: (400 + 64 + 320) = 784 or Option 2: (900 + 4 - 120) = 784.

If you are well aware of the 1 to 30 square values, you need to learn the square root from 1 to 30 numbers which will help you in mathematics calculations. You can read the 1 to 30 square root values by clicking on the link given below.

Square Root from 1 to 30-  Click to Read

Square 1 to 30 Solved Questions

Question 1: When a circular plate has a radius of 8 inches. Calculate the area of the plate in sq. inches.

Solution: Area of the circular plate (A) = πr² = π (8)²

By putting the value of the square of 8 from Square 1 to 30 chart;

i.e. A = 64π

Hence, the area of the circular plate = 201.14 inches².

Question 2: Calculate the area of a square carpet whose side is 5 inches.

Solution: Area of square carpet (A) = Side²

i.e. A = 5² = 25

Hence, the area of a square carpet is 25 inches².

Question 3: Two square-shaped books have sides of 6m and 8m respectively. Calculate the combined area of both books.

Solution: Area of book = (side)²

⇒ Area of 1st book = 6² = 36 m²

⇒ Area of 2nd book = 8² = 64 m²

Hence, the combined area of both the books is 36 + 64 = 100 m²

Question 4: Calculate the addition of the first 10 odd numbers.

Solution: The addition of the first n odd numbers is expressed as n²

⇒ Addition of first 10 odd numbers (n) = 10²

By putting the value of the square of 10 from squares 1 to 30 chart, 

The sum of the first 10 odd numbers = 100

Question 5: Find the total surface area of a spherical ball that has a radius of 5 cm.

Solution: As we know the total surface area of a sphere (A) = 4π r²  square units.

A =  4π( 5) ² cm²

A = 100 π  cm² = 314 cm²

Square 1 to 30: FAQs

Ans. The square of numbers from 1 to 30 covers the list of squares of all the numbers coming in the range of 1 to 30. The value of squares of numbers from 1 to 30 includes the range from 1 to 900.

Ans. The odd numbers within 1 to 30 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29. As the squares of odd numbers result in always odd. Hence, the squares of numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29 will be odd.

Ans. The sum of all perfect square numbers from 1 to 30 is 55 i.e. 1 + 4 + 9 + 16 + 25 = 55.

Ans. There are 2 methods namely multiplication by itself or using basic algebraic formulas for calculating the values of squares of numbers ranging from 1 to 30.

Ans. The even numbers present within 1 to 30 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30. As the squares of even numbers results in always even. Hence, the squares of numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30 will be even.

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