Square 1 to 30 – The square of a number is the many of the number with itself. Learning these squares assists applicants to simply solve different arithmetic issue & assists them to solve complex calculations with ease. The value of the square of 1 to 30 ranges from 1 to 900 & we speak for these squares in the exponent notation as, (a)2 where a is any number between 1 to 30 for instance, (11)2 then its value is calculating as, (11)2 = 11×11 = 121.
In this writing, we’ll learn regarding, the square of numbers from 1 to 30, the square 1 to 30 chart, sample & others in information.
Square 1 to 30
These square assist to simple solve many mathematical calculations, so it’s suggesting to learn all the squares to excel in mathematics classes.
- Exponent Form = x2
- Lowest Value = (1)2 = 1
- Highest Value = (30)2 = 900
So, the Range = 1 – 900
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Square 1 to 30 Table
The square of the 1st 30 natural numbers provided in the image talked about beneath –
| 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 & 30. Learning the square of even numbers from 1 to 30 is very significant. The following table hold 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 |
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Squares from 1 to 30 (Odd Numbers)
Learning the squares of odd numbers from 1 to 30 is very notable. 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 |
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Calculating Squares 1 to 30
The squares 1 to 30 can simply planned utilizing the 2 way as talked about beneath:
- Multiplication by Itself
- Utilizing Algebraic Identities
Now let us learn about these two way thoroughly.
Method 1:- Multiplication by Itself
Multiplying by itself means to search 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 calculating as (a)2 = a × a. Square of some numbers between 1 to 30 utilizing the multiplication by itself way is,
- (4)2 = 4 × 4 = 16
- (7)2 = 7 × 7 = 49
- (12)2 = 12 × 12 = 144
- (21)2 = 21 × 21 = 441, etc
This way functions best for smaller ways but for searching the square of the larger numbers we utilize other ways, i.e. utilizing Algebraic Identities.
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Method 2:- Utilizing Algebraic Identities
As the name recommends utilizing algebraic identities utilizes the basic identities of the square, i.e. it utilizes
- (a + b)2 = a2 + b2 + 2ab
- (a – b)2 = a2 + b2 – 2ab
Now the provided number “n” is broken as per these identities as,
n = (a + b) or n = (a – b) in accordance with the number n & then the square is found utilizing the identities talked about upper. This can understand by the sample talked about beneath –
For instance, to search the square of 28, we can convey 28 in 2 methods,
Solution:
- (20 + 8)
To search the square of 28 we utilize 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 way is utilizing to find the square of a big number very easily.
Solved Examples on Squares of 1 to 30
Example 1:- Search the area of the circular park whose radius is 21 m.
Solution:
Provided,
Radius of Park = 21 m
Area of Circular Park(A) = πr2
A = π (21)2
Utilizing the square of 21 from the square of 1 to 30 table
212 = 441
A = 22/7(441)
A = 1386 m2
So, the area of the circular park is 1386 m2
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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
Utilizing the square of 25 from the square of 1 to 30 table
252 = 625
A = 625 cm2
Thus, the glass needed to cover the square window is 625 cm2
Example 3:- Simplify 112 – 52 + 212
Solution:
Utilizing Square of 1 to 30 table we obtain,
- 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
Frequently Asked Questions
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
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.
What is magic square chart?
A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., arranged such that the sum of the numbers in any horizontal, vertical, or main diagonal line is always the same number (Kraitchik 1942, p. 142; Andrews 1960, p. 1; Gardner 1961, p.
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