Square 1 to 50
Square 1 to 50 is the list of squares of all the numbers from 1 to 50. The value of squares from 1 to 50 ranges from 1 to 2500. Memorizing these values will help students to simplify the timeconsuming equations quickly. The Square 1 to 50 in the exponential form is expressed as (x)^{2}.
Squares 1 to 50:
 Exponent form: (x)^{2}
 Highest Value: 50^{2} = 2500
 Lowest Value: 1^{2} = 1
1.  Square 1 to 50 
2.  Square 1 to 50 PDF 
3.  How to Calculate Square 1 to 50? 
4.  FAQs 
Squares 1 to 50 Chart
Squares from 1 to 50
Learning squares 1 to 50 can help students to recognize all perfect squares from 1 to 2500 and approximate a square root by interpolating between known squares. The values of squares 1 to 50 are listed in the table below.
List of All Squares from 1 to 50 

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 
41^{2} = 1681 
42^{2} = 1764 
43^{2} = 1849 
44^{2} = 1936 
45^{2} = 2025 
46^{2} = 2116 
47^{2} = 2209 
48^{2} = 2304 
49^{2} = 2401 
50^{2} = 2500 
The students are advised to memorize these squares 1 to 50 values thoroughly for faster math calculations.
Square 1 to 50  Even Numbers
The table below shows the values of squares 1 to 50 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 
42^{2} = 1764 
44^{2} = 1936 
46^{2} = 2116 
48^{2} = 2304 
50^{2} = 2500 
Square 1 to 50  Odd Numbers
The table below shows the values of squares from 1 to 50 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 
41^{2} = 1681 
43^{2} = 1849 
45^{2} = 2025 
47^{2} = 2209 
49^{2} = 2401 
How to Calculate the Values of Squares 1 to 50?
In order to calculate the squares from 1 to 50, we can use any one of the following methods:
Method 1: Multiplication by itself.
Method 2: Using basic algebraic identities: To find the square of 34, we can express 34 as:
 Option 1: (30 + 4)
 Option 2: (40  6)
In the next step, we use the basic algebraic identity formula and get Option 1: [30² + 4² + (2 × 30 × 4)] or Option 2: [40² + 6²  (2 × 40 × 6)]. Solving the expressions further, we get Option 1: (900 + 16 + 240) = 1156 or Option 2: (1600 + 36  480) = 1156.
Solved Examples on Square 1 to 50

Example 1: If a circular tabletop has a radius of 20 inches. Find the area of the tabletop in sq. inches?
Solution:
Area of circular tabletop = πr^{2} = π (20)^{2}
Using values from square 1 to 50 chart;
i.e. A = 400π
Therefore, the area of the tabletop = 1256.64 inches^{2}.

Example 2: Find the area of a square window whose side length is 24 inches.
Solution:
Area of square window (A) = Side^{2}
i.e. A = 24^{2} = 576
Therefore, the area of a square window is 576 inches^{2}.

Example 3: Two square wooden planks have sides 11m and 12m respectively. Find the combined area of both the wooden planks?
Solution:
Area of wooden plank = (side)^{2}
⇒ Area of 1st wooden plank = 11^{2} = 121 m^{2}
⇒ Area of 2nd wooden plank = 12^{2 }= 144 m^{2}
Therefore, the combined area of wooden planks is 121 + 144 = 265 m^{2}

Example 4: Find the sum of the first 50 odd numbers.
Solution:
The sum of first n odd numbers is given as n²
⇒ Sum of first 50 odd numbers (n) = 50²
Using values from square 1 to 50 chart, the sum of first 50 odd numbers = 50² = 2500
FAQs on Square 1 to 50
What is the Value of Squares 1 to 50?
The value of square 1 to 50 is the list of numbers obtained by multiplying an integer(1  50) by itself. It will always be a positive number.
What are the Methods to Calculate Squares from 1 to 50?
We can calculate the square of a number by using the a² + b² + 2ab formula. For example (12)² can be calculated by splitting 12 into 10 and 2. Other methods that can be used to calculate squares from 1 to 50:
 Finding Square by Column Method
 Finding Squares by Diagonal Method
If you Take Squares from 1 to 50, how many of them will be Even Numbers?
The even numbers between 1 to 50 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50. Since the squares of even numbers are always even. Therefore, the value of squares of numbers 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50 will be even.
Using Squares 1 to 50 Chart, find the value of 2 plus 9 Square plus 3 Square.
The value of 9² is 81 and 3² is 9. So, 2 + 9² + 3² = 92. Hence, the 2 plus 9 Square plus 3 Square is 92.
How Many Numbers in Squares 1 to 50 are Odd?
The odd numbers between 1 to 50 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49. Since the squares of odd numbers are always odd. Therefore, the value of squares of numbers 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49 will be odd.
What is the Sum of all Perfect Squares from 1 to 50?
The sum of all perfect squares from 1 to 50 is 140 i.e. 1 + 4 + 9 + 16 + 25 + 36 + 49 = 140.
What Values of Squares from 1 to 50 are Between 1 and 10?
The values of squares 1 to 50 between 1 and 10 are 1² (1), 2² (4), and 3² (9).
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