[Maths Class Notes] on Square Root from 1 to 25 Pdf for Exam

Are you someone who is looking to understand what squares and square roots of a number are? or are you someone who is struggling to understand the difference between twice of a number and square of a number? If yes, then has brought Square Root from 1 to 25 – Value Table, Calculating Method, Solved Examples & FAQs to solve your confusion and to answer all your questions.  Let’s start by understanding the meaning of a square of a number.

When a number is multiplied by 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 off 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.

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 squares 1 to 30. Memorizing squares from 1 to 30 will help you to simplify your problems more quickly.

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.

• The 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 the square root of 4 is 2

32 =9, or the square root of 9 is 3

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

The symbol of the square root is [ sqrt{}]

Thus, the square root of 4 is represented as [ sqrt{4}] = 2 and that of 9 is represented as [ sqrt{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 Roots 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.

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:

These solved examples are provided for you to understand the steps of the solutions. You are expected to follow a similar pattern in the exam while solving the questions. Also, these examples will help you understand how the concepts are applied in practice.

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

Ans:

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)3  = 12

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

Ans: 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, [ sqrt{1521}] = 3 x 13 = 39

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

Quiz Time:

These questions will help you test your understanding of the concepts. Answers to these questions are not provided on purpose. You will have to use your brains and find them on your own. This exercise will help you to become self-reliant. If the need arises, you can seek reference from the above-solved questions

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 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?