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.
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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.
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