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Math Square 1 to 40 : Table, Perfect Squares, Chart and Examples

Square 1 to 40 : Table, Perfect Squares, Chart and Examples

Mar 16, 2026

Square 1 to 40

When you multiply a number by itself, the resulting number is a square, and if you are someone who is either appearing in a competitive exam or just wants to do well in math in school, knowing square 1 to 40 is a really important skill.

But manually multiplying every time, though quick, can actually take more time than needed to add up, and eventually, you will take more time than needed to complete your sums. But what if you had the squares from 1 to 40 memorised by heart? In this guide, we will give you a cheat sheet of square 1 to 40 while also giving strategies to figure them out quickly.

Perfect Square Table Chart 1 to 40

Here is a square table from 1 to 40, which you can keep handy for your exam preparation.

Number (n)	Square (n²)
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400
21	441
22	484
23	529
24	576
25	625
26	676
27	729
28	784
29	841
30	900
31	961
32	1024
33	1089
34	1156
35	1225
36	1296
37	1369
38	1444
39	1521
40	1600

What are the Squares from 1 to 40?

To put it simply, when you multiply a number by itself, the resulting number is called a square. When you multiply a number by itself, you get a square number. For instance, 7 times 7 equals 49, which is the square of 7. There are all the perfect squares between 1² and 40² in the list of squares from 1 to 40.

People use this idea a lot when they locate perfect squares, square roots, and solve quadratic equations. Square numbers are also useful for activities like mathematics, finding areas, and recognizing patterns.

Which Numbers 1 to 40 Are Perfect Squares?

A perfect square is a number that can be represented as the product of a whole number multiplied by itself (n × n). This means that its square root is also a whole number.

The perfect squares 1 to 40 are:

1, 4, 9, 16, 25, 36

1 = 1²
4 = 2²
9 = 3²
16 = 4²
25 = 5²
36 = 6²

The next square is 7² = 49, which is greater than 40, so it is not included in the 1–40 range.

1 to 40 Squares – Even Numbers

Even Number	Square (n²)
2	4
4	16
6	36
8	64
10	100
12	144
14	196
16	256
18	324
20	400
22	484
24	576
26	676
28	784
30	900
32	1024
34	1156
36	1296
38	1444
40	1600

1 to 40 – Odd Numbers

Odd Number	Square (n²)
1	1
3	9
5	25
7	49
9	81
11	121
13	169
15	225
17	289
19	361
21	441
23	529
25	625
27	729
29	841
31	961
33	1089
35	1225
37	1369
39	1521

Formula Used in Square 1 to 40

To find the square of any number “n,” use the following formula: n² = n × n

Formula in Algebraic equations :

(a + b)²
(a − b)²

If you need to calculate the sum of two squares, the formula is: n(n+1)(2n+1)/6

How to Calculate the Values of Squares 1 to 40?

There are easy ways to quickly find 1 to 40 square numbers:

Take the number and multiply it by itself. For instance, 18 squared is 18 times 18, which is 324.
Use identities in algebra. To calculate 23², write 23 as 20 + 3 and use (a + b)² = a² + 2ab + b²: 23² = 20² + 2 × 20 × 3 + 3² = 400 + 120 + 9 = 529
Learn how to finish numbers with patterns. For instance, all numbers that end in 5 have squares that end in 25.
Use square number tables like the one above to help you remember things quickly for tests.

Solved Examples on Square 1 to 40

Example 1: Find 27²

Solution:
27² = 27 × 27
= (20 + 7)²
= 20² + 2(20)(7) + 7²
= 400 + 280 + 49
= 729

Example 2: Find 34²

Solution:
34² = 34 × 34
= (30 + 4)²
= 30² + 2(30)(4) + 4²
= 900 + 240 + 16
= 1156

Example 3: A square playground has a side length of 18 meters. Find its area.

Solution:
Area of a square = side × side
= 18 × 18
= 324 m²

Example 4: What is the value of 35²?

A) 1125
B) 1225
C) 1325
D) 1425

Solution:

35² = 35 × 35 = 1225
Correct Answer: B

Example 5: Which of the following is equal to 32²?

A) 1024
B) 1044
C) 1004
D) 1084

Solution:

32² = 32 × 32 = 1024

Correct Answer: A

Conclusion

Knowing the squares from 1 to 40 by heart is about giving yourself a real advantage. Whether you’re tackling problems in school tests or any competitive exam, having these values at your fingertips saves precious time and reduces calculation errors.

Make it a habit to practice this table regularly. The investment of a few minutes each day will pay off significantly when you’re under exam pressure and need to solve problems quickly and accurately. Start memorizing today, and watch your problem-solving speed improve dramatically!