The concept of square roots is a fundamental aspect of mathematics that has intrigued both students and scholars for centuries. 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 4×4, 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 x². For example, the square of 8 is 8² means 64. So the value of the square of 8 is 64.
Squares from 1 to 30
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.
| 1 to 30 Square Table | |
| 1² = 1 | 2² = 4 |
| 3² = 9 | 4² = 16 |
| 5² = 25 | 6² = 36 |
| 7² = 49 | 8² = 64 |
| 9² = 81 | 10² = 100 |
| 11² = 121 | 12² = 144 |
| 13² = 169 | 14² = 196 |
| 15² = 225 | 16² = 256 |
| 17² = 289 | 18² = 324 |
| 19² = 361 | 20² = 400 |
| 21² = 441 | 22² = 484 |
| 23² = 529 | 24² = 576 |
| 25² = 625 | 26² = 676 |
| 27² = 729 | 28² = 784 |
| 29² = 841 | 30² = 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.
- 2² = 4
- 4² = 16
- 6² = 36
- 8² = 64
- 10² = 100
- 12² = 144
- 14² = 196
- 16² = 256
- 18² = 324
- 20² = 400
- 22² = 484
- 24² = 576
- 26² = 676
- 28² = 784
- 30² = 900
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.
- 1² = 1
- 3² = 9
- 5² = 25
- 7² = 49
- 9² = 81
- 11² = 121
- 13² = 169
- 15² = 225
- 17² = 289
- 19² = 361
- 21² = 441
- 23² = 529
- 25² = 625
- 27² = 729
- 29² = 841
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 the 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;
ie 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 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