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Square 1 to 40
Square 1 to 40 is the list of squares of all numbers from 1 to 40. The values of squares from 1 to 40 range from 1 to 1600. Memorizing these values can help students in simplifying the timeconsuming math equations quickly. The square of a number x in the exponential form is expressed as (x)^{2}.
Square 1 to 40:
 Exponent form: (x)^{2}
 Highest Value: 40^{2} = 1600
 Lowest Value: 1^{2} = 1
1.  Square 1 to 40 
2.  Square 1 to 40 PDF 
3.  How to Calculate Square 1 to 40? 
4.  FAQs 
Squares 1 to 40 Chart
What are Squares From 1 to 40?
Learning the values of squares 1 to 40 can help students to recognize all the perfect squares from 1 to 1600 and approximate a square root by interpolating between known squares. The values of squares 1 to 40 are listed in the table below.
List of All Squares from 1 to 40 


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 
31^{2} = 961 
32^{2} = 1024 
33^{2} = 1089 
34^{2} = 1156 
35^{2} = 1225 
36^{2} = 1296 
37^{2} = 1369 
38^{2} = 1444 
39^{2} = 1521 
40^{2} = 1600 
Check the above square 1 to 40 PDF. The students are advised to download the PDF and keep it handy and also to memorize these squares 1 to 40 values thoroughly for faster math calculations.
1 to 40 Squares  Even Numbers
The even numbers from 1 to 40 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, and 40. The table below shows the values of squares 1 to 40 for even numbers.
2^{2} = 4 
4^{2} = 16 
6^{2} = 36 
8^{2} = 64 
10^{2} = 100 
12^{2} = 144 
14^{2} = 196 
16^{2} = 256 
18^{2} = 324 
20^{2} = 400 
22^{2} = 484 
24^{2} = 576 
26^{2} = 676 
28^{2} = 784 
30^{2} = 900 
32^{2} = 1024 
34^{2} = 1156 
36^{2} = 1296 
38^{2} = 1444 
40^{2} = 1600 
1 to 40 Squares  Odd Numbers
The odd numbers from 1 to 40 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, and 39. The table below shows the values of squares from 1 to 40 for odd numbers.
1^{2} = 1 
3^{2} = 9 
5^{2} = 25 
7^{2} = 49 
9^{2} = 81 
11^{2} = 121 
13^{2} = 169 
15^{2} = 225 
17^{2} = 289 
19^{2} = 361 
21^{2} = 441 
23^{2} = 529 
25^{2} = 625 
27^{2} = 729 
29^{2} = 841 
31^{2} = 961 
33^{2} = 1089 
35^{2} = 1225 
37^{2} = 1369 
39^{2} = 1521 
How to Calculate the Values of Squares 1 to 40?
To calculate the squares of 1 to 40, 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 3 = 3 × 3 = 9. Here, the resultant product “9” gives us the square of the number “3”. This method works well for smaller numbers.
Method 2: Using basic algebraic identities: To find the square of 23, we can express 23 as:
 Option 1: (20 + 3)
 Option 2: (30  7)
In the next step, we use the basic algebraic identity formula and get Option 1: [20^{2} + 3^{2} + (2 × 20 × 3)] or Option 2: [30^{2} + 7^{2}  (2 × 30 × 7)]. Solving the expressions further, we get Option 1: (400 + 9 + 120) = 529 or Option 2: (900 + 49  420) = 529.
Solved Examples on Square 1 to 40

Example 1: If a circular tabletop has a radius of 40 inches. Find the area of the tabletop in sq. inches? [π = 3.14]
Solution:
Area of circular tabletop = πr^{2} = π (40)^{2}
Using values from square table 1 to 40;
i.e. A = 1600π
Answer: ∴ The area of the tabletop = 5024 inches^{2}.

Example 2: Find the area of a square window whose side length is 32 inches.
Solution:
Area of square window (A) = Side^{2}
i.e. A = 32^{2} = 1024
Answer: The area of a square window is 1024 inches^{2}.

Example 3: Two square wooden planks have sides 20m and 25m respectively. Find the combined area of both wooden planks?
Solution:
Area of wooden plank = (side)^{2}
⇒ Area of 1^{st} wooden plank = 20^{2} = 400 m^{2}
⇒ Area of 2^{nd} wooden plank = 25^{2 }= 625 m^{2}
Answer: ∴ Combined area of wooden planks is 400 + 625 = 1025 m^{2}

Example 4: Find the sum of the first 40 odd numbers.
Solution:
The sum of first n odd numbers is given as n^{2}
⇒ Sum of first 40 odd numbers (n) = 40^{2}
Using values from squares of 1 to 40 chart, the sum of first 40 numbers = 40² = 1600
Answer: The sum of the first 40 odd numbers is 1600.
FAQs on Square 1 to 40
What is the Value of Squares 1 to 40?
The square 1 to 40 is the list of numbers obtained by multiplying an integer two times (y × y). It will always be a positive number. Here are the values of squares from 1 to 40.
 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
 31^{2} = 961; 32^{2} = 1024; 33^{2} = 1089; 34^{2} = 1156; 35^{2} = 1225; 36^{2} = 1296; 37^{2} = 1369; 38^{2} = 1444; 39^{2} = 1521; 40^{2} = 1600
What are the Methods to Calculate Squares from 1 to 40?
We can calculate the square of a number by using the (a + b)² formula. For example (16)² can be calculated by splitting 16 into 10 and 6. Other methods that can be used to Calculate squares from 1 to 40:
 Finding Square by Column Method
 Finding Squares by Diagonal Method
Using the Squares 1 to 40 Chart, Find the Value of 3 plus 10 Square plus 12 Square.
The value of 10^{2} is 100 and 12^{2} is 144. So, 3 + 10^{2} + 12^{2} = 253. Hence, the 3 plus 10 Square plus 12 Square is 253.
If you Take Squares from 1 to 40, How Many of Them Will be Even Numbers?
The even numbers between 1 to 40 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40. Since the squares of even numbers are always even. Therefore, the values of the squares of these numbers will be even.
How Many Numbers in Square Table 1 to 40 are Odd?
The odd numbers between 1 to 40 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39. Since the squares of odd numbers are always odd, the squares of these numbers will be odd.
What Values of Squares 1 to 40 are Between 1 and 15?
The values of squares 1 to 40 between 1 and 15 are 1^{2} (1), 2^{2} (4), and 3^{2} (9).
What is the Sum of all Perfect Squares from 1 to 40?
The sum of all perfect squares from 1 to 40 is 91 i.e. 1 + 4 + 9 + 16 + 25 + 36 = 91.
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