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Square 1 to 30
Squares 1 to 30 is the list of squares of all the numbers from 1 to 30. The value of squares from 1 to 30 ranges from 1 to 900. Memorizing these values will help students to simplify the timeconsuming equations quickly. The squares from 1 to 30 in the exponential form are expressed as (x)^{2}.
Squares from 1 to 30
 Exponent form: (x)^{2}
 Highest Value: 30^{2} = 900
 Lowest Value: 1^{2} = 1
1.  What are Squares from 1 to 30? 
2.  Square 1 to 30 PDF 
3.  How to Calculate Square 1 to 30? 
4.  FAQs on Square Numbers 1 to 30 
Squares 1 to 30 Chart
The following chart shows the square table 1 to 30 which helps the students in memorizing it easily.
What are Squares from 1 to 30?
Learning squares 1 to 30 can help students to recognize all perfect squares from 1 to 900 and approximate a square root by interpolating between known squares. The values of squares 1 to 30 are listed in the table below.
List of All Squares from 1 to 30 

1^{2} = 1 
2^{2} = 4 
3^{2} = 9 
4^{2} = 16 
5^{2} = 25 
6^{2} = 36 
7^{2} = 49 
8^{2} = 64 
9^{2} = 81 
10^{2} = 100 
11^{2} = 121 
12^{2} = 144 
13^{2} = 169 
14^{2} = 196 
15^{2} = 225 
16^{2} = 256 
17^{2} = 289 
18^{2} = 324 
19^{2} = 361 
20^{2} = 400 
21^{2} = 441 
22^{2} = 484 
23^{2} = 529 
24^{2} = 576 
25^{2} = 625 
26^{2} = 676 
27^{2} = 729 
28^{2} = 784 
29^{2} = 841 
30^{2} = 900 
The students are advised to memorize these squares 1 to 30 values thoroughly for faster math calculations. The link given above shows square 1 to 30 pdf which can be easily downloaded for reference.
Squares from 1 to 30  Even Numbers
The even numbers from 1 to 30 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30. The following table shows the values of squares 1 to 30 for even numbers.
2^{2} = 4 
18^{2} = 324 
4^{2} = 16 
20^{2} = 400 
6^{2} = 36 
22^{2} = 484 
8^{2} = 64 
24^{2} = 576 
10^{2} = 100 
26^{2} = 676 
12^{2} = 144 
28^{2} = 784 
14^{2} = 196 
30^{2} = 900 
16^{2} = 256 
1 to 30 Squares  Odd Numbers
The odd numbers from 1 to 30 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29. The following table shows the values of squares from 1 to 30 for odd numbers.
1^{2} = 1 
17^{2} = 289 
3^{2} = 9 
19^{2} = 361 
5^{2} = 25 
21^{2} = 441 
7^{2} = 49 
23^{2} = 529 
9^{2} = 81 
25^{2} = 625 
11^{2} = 121 
27^{2} = 729 
13^{2} = 169 
29^{2} = 841 
15^{2} = 225 
How to Calculate the Values of Squares 1 to 30?
In order to calculate the squares of 1 to 30, we can use any one of the following methods:
Method 1: Multiplication by itself
In this method, the number is multiplied by itself and the resultant product gives us the square of that number. For example, the square of 4 = 4 × 4 = 16. Here, the resultant product '16' gives us the square of the number '4'. This method works well for smaller numbers.
Method 2: Using basic algebraic identities
In this method, a given number ‘n’ is first expressed in the form of either (a+b) or (ab), where ‘a’ is a multiple of 10 and ‘b' is any number less than 10. Next, the basic algebraic identities formula is used to find the square of the given number. We can use any of the 2 basic algebraic identities formulas to calculate the square of a given number. (a + b)² = a² + b² + 2ab or (a  b)² = a² + b²  2ab. The form where ‘b’ has a smaller value should be preferred.
For example, to find the square of 29, we can express 29 as
 Option 1: (20 + 9)
 Option 2: (30  1)
In the next step, we use the basic algebraic identity formula and get Option 1: [20² + 9² + (2 × 20 × 9)] or Option 2: [30² + 1²  (2 × 30 × 1)]. Solving the expressions further, we get Option 1: (400 + 81 + 360) = 841 or Option 2: (900 + 1  60) = 841.
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Solved Examples on Squares of 1 to 30

Example 1: If a circular tabletop has a radius of 16 inches, what is the area of the tabletop in sq. inches?
Solution:
Area of circular tabletop = πr^{2} = π (16)^{2}
Let us use the values from the squares of 1 to 30 chart and we get 16^{2} = 256
Area = 256π
Therefore, the area of the tabletop = 804.57 inches^{2}.

Example 2: Find the area of a square window whose side length is 25 inches.
Solution:
Area of the square window (A) = Side^{2}
Using the square table 1 to 30, we get, Area = 25^{2} = 625
Therefore, the area of the window is 625 inches^{2}

Example 3: Two square wooden planks have sides 10 m and 12 m respectively. Find the combined area of both the wooden planks?
Solution:
Area of wooden plank = (side)^{2}
Let us use the chart of squares upto 30 to solve this question.
⇒ Area of 1st wooden plank = 10^{2} = 100 m^{2}
⇒ Area of 2nd wooden plank = 12^{2} = 144 m^{2}
Therefore, the combined area of wooden planks is 100 + 144 = 244 m^{2}

Example 4: What is the square of 15?
Solution:
Using values from square table 1 to 30 chart, we can get the square of 15 which is 15² = 225
FAQs on Square Numbers 1 to 30
What is the Value of Squares 1 to 30?
The value of squares upto 30 is the list of numbers obtained by multiplying an integer by itself. When we multiply a number by itself we will always get a positive number. For example, the square of 12 is 12^{2} = 144.
What are the Methods to Calculate Squares from 1 to 30?
We can calculate the square of a number by using the a² + b² + 2ab formula. For example (19)² can be calculated by splitting 19 into 10 and 9. Other methods that can be used to calculate squares from 1 to 30 are as follows:
 Finding Squares by Column Method
 Finding Squares by Diagonal Method
If You Take Squares from 1 to 30, How Many of Them Will be Even Numbers?
The even numbers between 1 to 30 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, and 30. Since the squares of even numbers are always even, therefore, the value of the squares of all these numbers will also be even.
Using Squares 1 to 30 Chart, Find the Value of 31 plus 30 Square plus 21 Square.
Using the chart of squares up to 30, we know that the value of 30² is 900 and 21² is 441. So, 31 + 30² + 21² = 1372. Hence, the value of 31 plus 30 Square plus 21 Square is 1372.
How Many Numbers in the Square Table 1 to 30 are Odd?
The odd numbers between 1 to 30 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, and 29. Since the squares of odd numbers are always odd. Therefore, the value of squares of all these numbers will also be odd.
What is the Sum of all Perfect Squares from 1 to 30?
The sum of all perfect squares from 1 to 30 is 55, i.e., 1 + 4 + 9 + 16 + 25 = 55.
What Values of Squares from 1 to 30 are Between 1 to 100?
The values of squares 1 to 30 between 1 to 100 are as follows. 1 = 1², 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = (81), and 10² = (100).
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