Square Root from 1 to 25

Square 1 to 30

When a number is multiplied with itself, the product is called the square of that number.

The square of a number is expressed as the number to the power 2 and it is pronounced as squared of a number.

Like this:

22 = 4 pronounced as 2 squared

And read as 2 squared equals 4

For Example, 

2 x 2 = 4 or 22  = 4. Thus, the square of 2 is 4. 

Similarly, 3 x 3 = 9  or 32 = 9,

    4 x 4 = 16 or 42 = 16,

    5 x 5 = 25 or 52 = 25, etc.

Square numbers are also called perfect squares.

  • A Natural number is said to be a perfect square, if it is the square of another natural number.

For ex., 5 x5 = 52 = 25, 6 x 6 = 62 = 36, 7 x7 = 72= 49, etc.

So we can say that 4, 9, 16, 25, 36, ……. are all perfect squares.

Squares Up to 30

The table below shows the values for square 1 to 30. Memorizing square 1 to 30 will help you to simplify your problems more quickly.

Natural Number 

Square

Natural Number

Square

Natural Number

Square

1

1

11

121

21

441

2

4

12

144

22

484

3

9

13

169

23

529

4

16

14

196

24

576

5

25

15

225

25

625

6

36

16

256

26

676

7

49

17

289

27

729

8

64

18

324

28

784

9

81

19

361

29

841

10

100

20

400

30

900


Properties of Square Numbers:

  • In 1 to 30 squares you notice that a number ending with 2, 3, 7 or 8 can never be a perfect square.

  • At the end of a perfect square, the number of zeros is always even.

  • Square of an even number is always even and the square of an odd number is always odd.

  • The Square of any real number always remains positive.

Methods of Finding the Squares:

Square of a number can be found in two ways

  • Column method

  • Diagonal method

Square Roots

The square root of a number x is that number which when multiplied by itself gives the number x itself. The number x under consideration is a perfect square.


For Example, 22 =4, or square root of 4 is 2

       32 =9, or square root of 9 is 3

     42 = 16, or the square root of 16 is 4

The symbol of the square root is √ 

Thus, the square root of 4 is represented as √ 4 = 2 and that of 9 is represented as √ 9 = 3

and so on.

Just as the division is the inverse operation of multiplication, the square root is the inverse operation of squaring a number. 


Note: Every square number can have a positive or negative square root.

Square Root 1 to 30

Square Root 1 to 30 will help you to solve the most time consuming long equations within no time, Square roots of 1 to 25 are listed in the table below.

Square Root of a Number

Number 

Square Root of a Number

Number

√4

2

√196

14

√9

3

√225

15

√16

4

√256

16

√25

5

√289

17

√36

6

√324

18

√49

7

√361

19

√64

8

√400

20

√81

9

√441

21

√100

10

√484

22

√121

11

√529

23

√144

12

√576

24

√169

13

√625

25

Properties of Square Root:

  • If the unit digit of a number is 2,3, 7 and 8 then it does not have a square root in natural numbers.

  • If a number ends in an odd number of zeros, then it does not have a square root in natural numbers.

  • The square root of an even number is even and that of an odd number is odd.

  • Negative numbers have no squares root in a set of real numbers.

Methods of Finding the Squares Roots:

Square of a number can be found in two ways

  1. Prime Factorisation Method

  2. Long Division method

Solved Examples:

Example 1: Find the value of √144 by the prime factorization method.

Solution:

Step 1: express 144 in prime factors

144 = 24 x 32

Step 2: Split the prime factors in two equal groups

144 = ( 23 x 3) x (23 x 3)

=(23 x 3)= 12

Example 2: The area of a square is 1521 cm2. Find the length of a side of the square by prime factorisation method.

Solution: Area of square = length x breadth

Therefore, Length of the square = √area

Now,     1521 = 32 x 132\

                      = (3 x 13) (3 x 13)

                      = (3 x 13)2

Therefore, √1521 = 3 x 13 = 39

The length of a side of the square is 39 cm.              

Quiz Time:

  1. The area of a square is 7225 cm2. Find the length of a side of the square by prime factorisation.

  2. Find the square root of 676 using the prime factorisation method and the long division method. Verify that the answer in both the cases is the same. 

  3. The area of a square tin plate is 7056 cm2. Find the length of a side of the plate.

  4. Can 8100 be a square number? Why or why not?

FAQ (Frequently Asked Questions)

1. Is 1 a Square Number?

Answer: Yes. When you multiply a number by itself we get the product as a Square number. Hence if we multiply 1 by itself we get 1, i.e 1 x 1 = 1.

1 is called a square number because it gives the area of a square with side length as an integer.

We can express it as a x a = a2 i.e 1 x 1 = 12 = 1.

2. What is Perfect Square?

Answer: A product of an integer with itself is said to be square or perfect square. Or in other words you can say that if any number is multiplied by itself it gives a perfect square.

For example 25 is a perfect square since it can be written as 25 = 5 x 5.

Perfect square is a number obtained by squaring two equal integers.

For testing if a given number is a perfect square or not we write the given number as the product of prime factors then we make pairs of the same factors.If there are factors all of which have a pair, then the given number is a perfect square.