Square 1 to 30

Square 1 to 30 is the square of all the natural numbers from 1 to 30. The square of a number is the multiple of the number with itself. Learning these squares helps students to easily solve various arithmetic problems and helps them to solve complex calculations with ease. The value of the square of 1 to 30 ranges from 1 to 900 and we represent these squares in the exponent notation as, (a)² where a is any number between 1 to 30 for example, (11)² then its value is calculated as, (11)² = 11×11 = 121.

In this article, we will learn about, the square of numbers from 1 to 30, the square 1 to 30 chart, examples, and others in detail.

Squares 1 to 30

The square from 1 to 30 is the square of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, and 30. These square helps to easily solve various mathematical calculations, so it is advised to learn all the squares to excel in mathematics classes. The square of the numbers from 1 to 30 ranges from 1 to 900, i.e.

• Exponent Form = x²
• Lowest Value = (1)² = 1
• Highest Value = (30)² = 900

Thus, the Range = 1 – 900

Squares 1 to 30 Chart

The chart containing all the values of the squares from 1 to 30 is added in the form of the image below:

Square 1 to 30 Table

The squares of numbers from 1 to 30 i.e the square of the first 30 natural numbers given in the image discussed below,

Number	Square	Number	Square	Number	Square
1	1	11	121	21	441
2	4	12	144	22	484
3	9	13	169	23	529
4	16	14	196	24	576
5	25	15	225	25	625
6	36	16	256	26	676
7	49	17	289	27	729
8	64	18	324	28	784
9	81	19	361	29	841
10	100	20	400	30	900

Squares from 1 to 30 (Even Numbers)

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 square of even numbers from 1 to 30 is very important. The following table contains the squares 1 to 30 for even numbers.

Even Numbers (1 to 30)	Square of Even Numbers (1 to 30)
2	(2)2 = 4
4	(4)2 = 16
6	(6)2 = 36
8	(8)2 = 64
10	(10)2 = 100
12	(12)2 = 144
14	(14)2 = 196
16	(16)2 = 256
18	(18)2 = 324
20	(20)2 = 400
22	(22)2 = 484
24	(24)2 = 576
26	(26)2 = 676
28	(28)2 = 784
30	(30)2 = 900

Squares from 1 to 30 (Odd Numbers)

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 odd numbers from 1 to 30 is very important. The following table shows the values of squares from 1 to 30 for odd numbers.

Odd Numbers (1 to 30)	Square of Odd Numbers (1 to 30)
1	(1)2 = 1
3	(3)2 = 9
5	(5)2 = 25
7	(7)2 = 49
9	(9)2 = 81
11	(11)2 = 121
13	(13)2 = 169
15	(15)2 = 225
17	(17)2 = 289
19	(19)2 = 361
21	(21)2 = 441
23	(23)2 = 529
25	(25)2 = 625
27	(27)2 = 729
29	(29)2 = 841

Calculating Squares 1 to 30

The squares 1 to 30 can easily be calculated using the two methods as discussed below:

• Multiplication by Itself
• Using Algebraic Identities

Now let’s learn about these two methods in detail.

Method 1: Multiplication by Itself

Multiplying by itself means to find the squares of the number we just multiply the number with itself, i.e. the square of any number a is (a)² then it is calculated as (a)² = a × a. Square of some numbers between 1 to 30 using the multiplication by itself method is,

• (4)² = 4 × 4 = 16
• (7)² = 7 × 7 = 49
• (12)² = 12 × 12 = 144
• (21)² = 21 × 21 = 441, etc

This method works best for smaller methods but for finding the square of the larger numbers we use other methods, i.e. using Algebraic Identities.

Method 2: Using Algebraic Identities

As the name suggests using algebraic identities uses the basic identities of the square, i.e. it uses

• (a + b)² = a² + b² + 2ab
• (a – b)² = a² + b² – 2ab

Now the given number “n” is broken according to these identities as,

n = (a + b) or n = (a – b) according to the number n and then the square is found using the identities discussed above. This can be understood by the example discussed below,

For example, to find the square of 28, we can express 28 in two ways,

Solution:

• (20 + 8)

To find the square of 28 we use the algebraic identity,

(a + b)² = a² + b² + 2ab

(20 + 8)² = 20² + 8² + 2(20)(8)

= 400 + 64 + 320

= 784

• (30 – 2)

To find the square of 28 we use the algebraic identity,

(a – b)² = a² + b² – 2ab

(30 – 2)² = 30² + 2² – 2(30)(2)

= 900 + 4 – 120

= 784

This method is used to find the square of a large number very easily.

Read More,

• Squares and Square Roots
• Square Root Formula
• Square root of 2
• Square Root of 3

Solved Examples on Squares of 1 to 30

Example 1: Find the area of the circular park whose radius is 21 m.

Solution:

Given,

Radius of Park = 21 m

Area of Circular Park(A) = πr²

A = π (21)²

Using the square of 21 from the square of 1 to 30 table

21² = 441

A = 22/7(441)

A = 1386 m²

Thus, the area of the circular park is 1386 m²

Example 2: Find how much glass is required to cover the square window of side 25 cm.

Solution:

Given,

Side of Square Window(s) = 25 cm

Area of Square Window(A) = (s)²

A = (25)²

Using the square of 25 from the square of 1 to 30 table

25² = 625

A = 625 cm²

Thus, the glass required to cover the square window is 625 cm²

Example 3: Simplify 11² – 5² + 21²

Solution:

Using Square of 1 to 30 table we get,

• 11² = 121
• 5² = 25
• 21² = 441

Simplifying, 11² – 5² + 21²

= 121 – 25 + 441

= 562 – 25

= 537

Example 4: Simplify 16² + 15² – 19²

Solution:

Using Square of 1 to 30 table we get,

• 16² = 256
• 15² = 225
• 19² = 361

Simplifying, 16² + 15² – 19²

= 256 + 225 – 361

= 481 – 361

= 120

FAQs on Square Numbers 1 to 30

1. What is the Value of Squares 1 to 30?

The square of 1 to 30 is the square of all the numbers from 1 to 30, and they are added in the table below:

Number	Square	Number	Square	Number	Square
1	1	11	121	21	441
2	4	12	144	22	484
3	9	13	169	23	529
4	16	14	196	24	576
5	25	15	225	25	625
6	36	16	256	26	676
7	49	17	289	27	729
8	64	18	324	28	784
9	81	19	361	29	841
10	100	20	400	30	900

2. What are Methods to Calculate Squares from 1 to 30?

There are two methods to find the square from 1 to 30. They are,

• Multiplication by Itself
• Using Algebraic Identities

3. What is Square of 1 to 10?

The square of 1 to 10, i.e. the square of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 is added in the table below:

Number	Square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100

4. Why it is Important to Learn Square 1 to 30?

It is important for students to learn the square from 1 to 30 because it helps the students to easily solve various mathematical problems and helps them with their problems.