Squares 1 to 30 (original) (raw)

Last Updated : 5 Sep, 2025

A **square number is the product of a number multiplied by itself. It is commonly represented using exponent notation:

a2= a × a

Squares 1 to 30 Chart

Square-1-to-30

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

**Also check: Squares 1 to 50

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)	Squares 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)	Squares 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

Square of Negative Numbers

The square of a negative number is always positive because multiplying two negative numbers results in a positive product.
The square of a negative number results in a positive value, as shown in the table below:

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

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 square of the number we 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.

Perfect-Square

Example of Multiplying by itself

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.

Tricks to Memorize Squares

Here are some helpful tricks to assist you in memorizing square roots:

Squaring a number simply means multiplying it by itself.
Start by memorizing the most common squares (from 1 to 9).
For numbers ending in 5 (such as 5, 15, 25), use the equation: **n(n + 1), followed by 25.
For example, for 25:
2 × (2 + 1) = 6, followed by 25, giving you 625.
Apply the algebraic tricks mentioned above to make it easier.
For example: (29)2:
(30 − 1)2 = 302 × 30 × 1 + 12
292 = 900 − 60 + 1 = 841

**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 11 2 - 5 2 **+ 21 2

**Solution:

Using Square of 1 to 30 table we get,

112 = 121

52 = 25

212 = 441

Simplifying, **11 2 - 5 2 **+ 21 2
= 121 - 25 + 441
= 562 - 25
= 537

**Example 4: Simplify 16 2 + 15 2 **- 19 2

**Solution:

Using Square of 1 to 30 table we get,

162 = 256

152 = 225

192 = 361

Simplifying, **16 2 + 15 2 **- 19 2
= 256 + 225 - 361
= 481 - 361
= 120

Solved Question On Squares of 1 to 30

**Question 1: Find the area of a square window whose side length is 17 inches.

**Solution:

Area of the Square window (A) = Side2
Using the squaretable 1 to 30, we get,
Area = 172 = 289
Therefore, the area of the window is 289 inches

**Question 2: What is the square of 26?

**Solution:

Using the value from square table 1 to 30 chart,
we can get the square of 26 which is 262 = 676

**Question 3: Two square wooden planks have sides 5 m and 12 m,, respectively. Find the combined area of both wooden planks.

**Solution:

Area of wooden plank = (side)2
Let us use the chart of square upto 30 to solve this question

Area of 1st wooden plank = 52 = 25
Area of 2nd wooden plank = 102 = 100

Therefore, the combined area of wooden plank is 100 + 25 = 125 m2

**Question 4: If a circular tabletop has a radius of 25 inches, what is the area of the tabletop in sq. inches?

**Solution:

Area of circular tabletop = πr2 = π (25)2
Let us use the value from squares of 1 to 30 chart and we get
(25)2 = 625
Area = 625π

Therefore, the area of tabletop = 1963.50 inches2

Unsolved Question On Squares 1 to 30

**Question 1: Find the area of a square garden whose side length is 14 meters.

**Question 2: What is the square of 19?

**Question 3: Two square carpets have sides 8 m and 15 m, respectively. Find the combined area of both carpets.

**Question 4: A circular garden has a radius of 12 feet, what is the area of the garden in square feet?

**Answer Sheet

196 meters2

361

289 merters2

452.39 square feet