Methods to Calculate Square Root of 4 with Examples and FAQs

What is a square root?

The square root of a number is the number which, when multiplied to itself, gives the product, which is an original number.

 Let’s take an example

2×2 =4

Here 4 is a perfect square of 2, and the square root of 4 is 2.

The exact value of √4 is 2. Now the roots of √4 can be either positive or negative. Every number has two roots, positive and negative. Thus square root of 4  can be represented as 2 or -2. Thus to conclude, a square root of a number can be presented as ± 2.

 Every number has a square root. For non-square numbers, their square root does not tend to be in whole numbers.

let’s take an example

Square of A = B

A = √B

which means that A is the square root of B.

What do you mean by Perfect Square?

The natural numbers, which are squares of other natural numbers, are known as perfect squares.

The perfect square number has a whole number square root. The square root of 4 is 2, which means that a square root is a whole number, which means that 4 is a perfect square.

For example:

Following is a list of some Perfect square numbers.

Integer	Perfect square
2 x 2	4
3 x 3	9
4 x 4	16
5 x 5	25

Exponential Form & Radical Form

The Radical form of a number is expressed as 

Example: 

if a number is 4, radical form is √4

The Exponential form of a number is expressed as

Example:

If a number is 4, exponential form is 4½

 The square root of a number is Rational or Irrational 

A rational number is expressed as a ratio of two integers as a/b where b is not equal to 0.

Example

√4 =2

which means 2/1 as a/b

Thus the b is not equal to 0. Thus square root of 4 is a rational number.

If the square root of a number is not the whole number, then the square root of a number is an irrational number.

 How to find a square root of 4?

 To calculate the square root of a number, there are two methods:

• Prime Factorisation

• Long division method

Let’s understand how to calculate the square root of 4 through both the method given.

• Prime Factorisation

In prime factorisation methods, we find factors of a number given. Let’s understand it through our example.

Example: 

If the number is 4, divide 4 into its factors which are

4 = 2×2×1

√4= square of (2)

√4= ( square of 2)½

√4 = 2

which means the square root of 4 is 2.

• Long division method

In the Long division method, we place the number inside the division symbol; let’s understand with an example.

Example: 

If the number is 4,

 Step 1: Try to pair the numbers into pairs by placing a bar over it, i.e. for digits to the left of a decimal point, pair them from right to left.

 Step 2: Since the number is 4, We know that 2× 2 is 4 and equal 4. Now let’s divide 4 by 2. Find the largest number so that when you multiple the number to itself, the product is less than or equal to 4.

 Step 3: After the division of 4 by 2, the remainder is 0, and the quotient is 2. Thus the square root of 4 is 2, and the process of the long division gets completed. 

 FAQ’s on Square Root of 4

1. Why the square root of the number 4 is a rational number? 

Ans: The rational number is the form p/q, where q is not equal to 0. Thus the square root of 4 calculated through prime factorisation or long division method is 2, i.e. a whole number where q is equal to 1. Thus square root of 4 is a rational number.

2. Does number 4 has a perfect square?

Ans: Yes, number 4 has a perfect square. By prime factorisation, the factors of 4 are 2×2, i.e. pair of 2. Thus all the factors are in pairs; number 4 has a perfect square.

3 . What is the square root of 4 in the simplest radical form?

Ans:  Express number 4 in the form of its product of prime numbers, i.e. 4 = 2×2. Thus the radical form of the square root of 4 cannot be simplified further. Therefore the simplest radical form of the square root of 4 is expressed as √4.

4. The square root of 4 is a positive or negative number?

Ans: Every number has a positive and a negative square root. For number 4, the √4  is 2. It can be 2 and -2. It can also be presented as ± 2.

5. What are the methods to calculate the square root of a number?* 

Ans: There are two methods to calculate the square root of a number:

• Prime factorisation method 

• Long division method