A square of a number is calculated by multiplying a number by itself twice. Geometrically, a square is a two-dimensional plane that has equal sides.

Area of a square = Side × Side

Square number = a × a = a²

1, 4, 9, 16, 25, 36, 49, 64, etc. are some of the examples of the number for a square of a number. If S is a number that formed by multiplying a by two times, then S is called the square of a number. For example, 16 is a number then it can write as 4 . 4 where 4 is the natural number and 16 is the square of a number. Also, 42 is a number and it is the multiplication of 7 and 6. However, 42 is not considered as a square of a number. Square numbers are also treated as perfect square numbers.

## List of Square Concepts

We have given a list of Square Concepts and their concerned links for you. Click on the required link and learn the entire topic easily.

### Solved Examples on Square of a Number

Check the below examples to understand which numbers are called squares of a number.

- 2² = (2 × 2) = 4. Therefore, we can say that the square of 2 is 4.
- 3² = (3 × 3) = 9. Therefore, we can say that the square of 3 is 9.
- 4² = (4 × 4) = 16. Therefore, we can say that the square of 4 is 16.
- 5² = (5 × 5) = 25. Therefore, we can say that the square of 5 is 25.
- 6² = (6 × 6) = 36. Therefore, we can say that the square of 6 is 36.
- 7² = (7 × 7) = 49. Therefore, we can say that the square of 7 is 49.
- 8² = (8 × 8) = 64. Therefore, we can say that the square of 8 is 64.
- 9² = (9 × 9) = 81. Therefore, we can say that the square of 9 is 81.
- 10² = (10 × 10) = 100. Therefore, we can say that the square of 10 is 100.
- 11² = (11 × 11) = 121. Therefore, we can say that the square of 11 is 121.
- 12² = (12 × 12) = 144. Therefore, we can say that the square of 12 is 144.
- 13² = (13 × 13) = 169. Therefore, we can say that the square of 13 is 169.
- 14² = (14 × 14) = 196. Therefore, we can say that the square of 14 is 196.
- 15² = (15 × 15) = 225. Therefore, we can say that the square of 15 is 225.

### Square of a Negative Number

The square of a negative number always a positive number.

- (-2)² = ((-2) × (-2)) = 4. Therefore, we can say that the square of (-2) is 4.
- (-3)² = ((-3) × (-3)) = 9. Therefore, we can say that the square of (-3) is 9.
- (-4)² = ((-4) × (-4)) = 16. Therefore, we can say that the square of (-4) is 16.
- (-5)² = ((-5) × (-5)) = 25. Therefore, we can say that the square of (-5) is 25.
- (-6)² = ((-6) × (-6)) = 36. Therefore, we can say that the square of (-6) is 36.
- (-7)² = ((-7) × (-7)) = 49. Therefore, we can say that the square of (-7) is 49.
- (-8)² = ((-8) × (-8)) = 64. Therefore, we can say that the square of (-8) is 64.
- (-9)² = ((-9) × (-9)) = 81. Therefore, we can say that the square of (-9) is 81.
- (-10)² = ((-10) × (-10)) = 100. Therefore, we can say that the square of (-10) is 100.
- (-11)² = ((-11) × (-11)) = 121. Therefore, we can say that the square of (-11) is 121.
- (-12)² = ((-12) × (-12)) = 144. Therefore, we can say that the square of (-12) is 144.
- (-13)² = ((-13) × (-13)) = 169. Therefore, we can say that the square of (-13) is 169.
- (-14)² = ((-14) × (-14)) = 196. Therefore, we can say that the square of (-14) is 196.
- (-15)² = ((-15) × (-15)) = 225. Therefore, we can say that the square of (-15) is 225.

### What is the Square of a number?

A number is multiplied by itself to form a square of a number. Thus, the number with exponent 2 is called the square number.

Example:

\(\frac { 3 }{ 7 } \) × \(\frac { 3 }{ 7 } \) = (\(\frac { 3 }{ 7 } \))² = \(\frac { 9 }{ 49 } \)

Here \(\frac { 9 }{ 49 } \) is the square of \(\frac { 3 }{ 7 } \).

0.2 × 0.2 = (0.2)² = 0.04

Here 0.04 is the square of 0.2.

### Odd and Even Square numbers

- Square of an even number is always even, i.e, (2n)² = 4n².
- Square of an odd numbers is always odd, i.e, (2n + 1) = 4(n² + n) + 1.
- Since every odd square is of the form 4n + 1, the odd numbers that are of the form 4n + 3 are not square numbers.

### Properties of Square Numbers

Check out the properties of Square Numbers given below to completely understand the Square concept.

1. If the numbers 2, 3, 7, or 8 present in the unit’s place, then the number will not become a perfect square. Therefore, the numbers that end with 2, 3, 7, or 8 will never become a perfect square.

2. The number ends with even zeros becomes perfect squares. Also, the numbers with an odd number of zeros will never become a perfect square.

3. Square of even numbers always an even number and square of odd numbers always an odd number.

4. If the natural numbers that are more than one are squared, then it should be either of multiple of 3 or more than the multiple of 3 by 1.

5. Also, if the natural numbers that are more than one are squared, then it should be either of multiple of 4 or more than the multiple of 4 by 1.

6. If the unit’s digit of the square of a number is equal to the unit’s digit of the square of the digit at the unit’s place of the given natural number.

7. If there are n natural numbers, say x and y such that x² = 2y².

8. For every natural number n, we can write it as (n + 1)² – n² = ( n + 1) + n.

9. For any natural number, say”n” which is greater than 1, we can say that (2n, n² – 1, n²+ 1) should be a Pythagorean triplet.

10. If a number n is squared, it equals the sum of first n odd natural numbers.