Square Numbers

Square Numbers are the product of a number multiplied by itself. These are fundamental to mathematics. In this article, we will explain Square Numbers, Give Examples, List of Square Numbers from 1 to 100, Why are they called Square Numbers and others in detail.

What is a Square Number?

Square Numbers are numbers that are the square of an integer. It means any number that is square of a number is called a square number. Suppose we take a number 100 that is square of 10 then 100 is a square number. Mathematically, Square Number Definition is,

“Result of multiplying an integer by itself is an integer known as a square number. It is the product of multiplying a number by itself.”

Square Numbers are always positive numbers. We know that,

(+) × (+) = (+)

(-) × (-) = (+)

For example, (-3)² = 9.

Examples of Square Numbers

As we know, square numbers are those that result from multiplying an integer by itself. Here are some examples:

• 1² = 1
• 12² = 144
• 15² = 225
• 25² = 625
• 49² = 2401
• 81² = 6561

List of Square Numbers

List of all some square numbers are,

Number	n × n = n2	Square number (n2)
1	1 × 1 = 12	1
2	2 × 2 = 22	4
3	3 × 3 = 32	9
4	4 × 4 = 42	16
5	5 × 5 =52	25

Square 1 to 30 Chart

Square 1 to 30 chart is added in form of image below,

Square Number in Geometry

Square shape in geometry has all its sides equal. Area of Square is equal to the square of its side.

Area of a Square = Side × Side = Side²

Square Number = a × a = a²

Formula of Square Number

Square of a Number is calculated using the formula,

Square Number of n = n × n = n² (where “n” is an Integer)

For example, Square of 3 = (3)² = 9

Any real number may be squared using this formula, which just requires multiplying the number by itself.

Types of Square Numbers

Various square number types are,

• One Digit Square Numbers: One digit numbers that are perfect square are called one digit square numbers. For example, 1, 4, 9 are one digit square numbers.

• Two Digit Square Number: Two digit numbers that are perfect square are called two digit square numbers. For example, 16, 25, 36, etc. are two digit square numbers.

• Three Digit Square Number: Three digit numbers that are perfect square are called three digit square numbers. For example, 121, 144, 169, etc. are three digit square numbers.

Apart, from these we can have Four Digit Square Numbers, Five Digit Square numbers, etc.

Perfect Square Numbers from 1 to 100

Integers with perfect square values between 1 and 100 can be written as the product of an integer times its own multiplication, yielding a whole number. Said another way, these figures represent the squares of whole numbers.

Since each number is expressed as the square of a certain integer, the list consists of

• 1² = 1
• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 6² = 36
• 7² = 49
• 8² = 64
• 9² = 81
• 10² = 100

Odd and Even Square Numbers

• Square of odd numbers are always odd numbers.
• Square of even numbers are always even numbers.

Odd Square Numbers: 1, 9, 25, 49, 81, …

Even Square Numbers: 4, 16, 36, 64, 100, …

How to Calculate Squares of a Number?

To find calculate square of number multiply a number n by itself (n × n = n²). For example,

3² = 3 × 3 = 9

7² = 7 × 7 = 49

Using this method squares of any number is easily found,

List of Square Numbers (1 to 50)

Square Numbers of 1 to 50 is added in the table below,

Number	Square	Number	Square
12	1	262	676
22	4	272	729
32	9	282	784
42	16	292	841
52	25	302	900
62	36	312	961
72	49	322	1024
82	64	332	1089
92	81	342	1156
102	100	352	1225
112	121	362	1296
122	144	372	1369
132	169	382	1444
142	196	392	1521
152	225	402	1600
162	256	412	1681
172	289	422	1764
182	324	432	1849
192	361	442	1936
202	400	452	2025
212	441	462	2116
222	484	472	2209
232	529	482	2304
242	576	492	2401
252	625	502	2500

Square Numbers from 51 to 100

Square from 51 and 100 are added in the table below,

Number	Square	Number	Square
512	2601	752	5625
522	2704	762	5776
532	2809	772	5929
542	2916	782	6084
552	3025	792	6241
562	3136	802	6400
572	3249	812	6561
582	3364	822	6724
592	3481	832	6889
602	3600	842	7056
612	3721	852	7225
622	3844	862	7396
632	3969	872	7569
642	4096	882	7744
652	4225	892	7921
662	4356	902	8100
672	4489	912	8281
682	4624	922	8464
692	4761	932	8649
702	4900	942	8836
712	5041	952	9025
722	5184	962	9216
732	5329	972	9409
742	5476	982	9604
752	5625	992	9801
762	5776	1002	10000

Properties of Square Numbers

Various properties of square number are listed as follows:

Square Numbers Symbol

• Symbol of Square is Superscript 2, such as n²

Odd Square and Even Square

• Square of odd number is always an odd number, and square of even number is always an odd numbers. Example: 4² = 16 (even), 3² = 9 (odd).
• Sum of Consecutive Odd Numbers: Sum of first n odd numbers is equal to n².
• Square Roots: Square root of a square number are always integers. For example, √16 = 4

Why are They Called ‘Square’ Numbers?

Square numbers are square numbers because they are square of various integers, such as, 12² = 144 and (-9)² = 81.

Square Roots

Square numbers are found when we multiply an integer is multiplied by itself. Square roots is opposite of this operation, squre roots are number which when multiplied by itself gives the original number.

For example,

• 8 × 8 = 64
• √(64) = 8

We can say that, square root of any number is a number which when squared gets the original number.

Read More,

• Perfect Cubes
• Square 1 to 30

Examples on Square Numbers 1 to 100

Example 1: What is square of 8?

Solution:

Square of 8 (8²) is 64

Example 2: Find square of 15.

Solution:

Square of 15 (15)² equals 225

Example 3: What is square of 25?

Solution:

Square of 25 is (25)² is 625

Example 4: Simplify 13² + 5² – 11²

Solution:

= 13² + 5² – 11²

= 169 + 25 – 121

= 73

Practice Questions on Square Numbers

Some problems on square numbers are,

Q1: Find the minimum number that must be subtracted from 8000 for the result to be a perfect square?

Q2: If two consecutive perfect squares have a product that is a perfect square, find the two squares?

Q3: Can a perfect square be created by adding two consecutive perfect cubes? If so, find it; if not, explain yourself?

Frequently Asked Questions on Square Numbers

What is a Square Number?

Multiplying an integer by itself yields a square number. It is that integer squared. For instance, 3×3=9 indicates that 9 is a square number.

What is Process for Finding a Square of Number?

Multiplying an integer by itself yields the square of that value. Writing n2 is the notation for a number n’s square. As an example, 72 is equal to 7 times 7 and 49.

What are First Five Integers Square?

Square of first five integers are,

• 1² = 1
• 2² = 4
• 3² = 9
• 4² =16
• 5² = 25

What is Square of Zero?

Square of zero (0)² = 0, 0 is a square number.

What is 100 Squared?

(100)² = 10000