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.

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.

Square of a number can be found in two ways

Column method

Diagonal method

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 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.

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.

Square of a number can be found in two ways

Prime Factorisation Method

Long Division method

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)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.

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

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.

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

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 = a^{2} 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.