What are Perfect Squares in Math? (List of Perfect Square Numbers) – BYJUS

# Perfect Squares

Powers are used to represent the repeated multiplication of a number by itself. When the exponent of a power is two, the value of the power is a perfect square. Perfect squares are a particular type of number. In this article, we will understand the concept of perfect squares and also learn methods to identify them....Read MoreRead Less

## About Perfect Square ## What is a Perfect Square?

Perfect squares are numbers that are the products of integers by themselves. In other words, when an integer is multiplied by itself, the resulting product is termed as a perfect square of the given number.

For example, 36 is a perfect square because it is the product of 6 by itself, 6$$\times$$6 = 36. So, we can express a perfect square as p$$^2$$, where p is an integer. ## A List of Perfect Squares

Natural number

Perfect square

1

1 $$\times$$ 1 = 1

2

2 $$\times$$ 2 = 4

3

3 $$\times$$ 3 = 9

4

4 $$\times$$ 4 = 16

5

5 $$\times$$ 5 = 25

6

6 $$\times$$ 6 = 36

7

7 $$\times$$ 7 = 49

8

8 $$\times$$ 8 = 64

9

9 $$\times$$ 9 = 81

10

10 $$\times$$ 10 = 100

11

11 $$\times$$ 11 = 121

12

12 $$\times$$ 12 = 144

13

13 $$\times$$ 13 = 169

14

14 $$\times$$ 14 = 196

15

15 $$\times$$ 15 = 225

16

16 $$\times$$ 16 = 256

17

17 $$\times$$ 17 = 289

18

18 $$\times$$ 18 = 324

19

19 $$\times$$ 19 = 361

20

20 $$\times$$ 20 = 400

21

21 $$\times$$ 21 = 441

22

22 $$\times$$ 22 = 484

23

23 $$\times$$ 23 = 529

24

24 $$\times$$ 24 = 576

25

25 $$\times$$ 25 = 625

## Solved Perfect Square Examples

Example 1: The area of a circle is 45,216 square feet. What is the radius of the circle?

Solution:

Given, the area of the circle = 45,216 square feet

The area of a circle $$A=r^2$$

$$45,216=3.14~r^2$$

$$r^2=\frac{45,216}{3.14}=14400$$

$$r=\sqrt{14400}$$

$$r=120$$ feet

Hence, the radius of the circle is 120 feet.

Example 2: Find the perfect square of 15.

Solution:

Given number = 15

To find the perfect square, multiply the number by itself

Therefore, 15 $$\times$$ 15 = 225

Hence, the perfect square of 15 is 225.

Example 3: Evaluate the expression $$5\sqrt{9}+10$$.

Solution:

Given expression, $$5\sqrt{9}+10$$

Since the square of 3 is 9, that is, $$\sqrt{9}=3$$

So, $$5\sqrt{9}+10$$

= $$5\times3+10$$

= 15 + 10

= 25

Hence, $$5\sqrt{9}+10=25$$.

Frequently Asked Questions on Perfect Squares

There are four perfect squares between 1 and 20: $$1^2,2^2,3^2,$$ and $$4^2$$.

They are: 1, 4, 9, 16.

Yes, 196 is a perfect square of 14, $$14^2=196$$

A number is a perfect square if the square root of the number is an integer. The square root of 120 is approximately 10.954. The square root of 120 is not an integer. Hence, 120 is not a perfect square.

The perfect square of 25 is 625, that is, $$25^2=625$$.

A number is considered to be a perfect square if it can be written as a square of an integer, that is, if it is a product of a number when multiplied by the number itself.