Square Root of 4

Square Root of 4 is equal to 2. It is represented as √(4) or (4)^1/2. The Square Root of a number is defined as the number that when multiplied by itself gives the original number.

In this article, we will learn what is the value of the square root of 4, how to find the value of the square root of 4.

Square Root of 4 Value

When we talk about the square root of 4, we’re looking for a special number that, when multiplied by itself, gives us the original number we started with.

Square Root of 4 = 2

If we multiply 2 with 2, we get 4 as (2 × 2 = 4).

So, for 4, 2 is the only special number from which when we multiply we get 4. The square root of 4 is 2.

How to Find Square Root of 4?

To find square root as we discuss earlier, we need to find a number if we multiply that number to itself, we get the original number. if we talk about the natural numbers if we multiply the natural numbers by itself then we get a perfect square.

We need to understand what are perfect Square, perfect Square are the number in which we get a unique whole number in which when we multiply that number by itself, we get that original number. Simply, The numbers in which their root is a whole number then that is a perfect square number. for example, if we talk about first five natural numbers, then we are going to find their perfect square below:

Natural Number	Perfect Square
1 × 1	1
2 × 2	4
3 × 3	9
4 × 4	16
5 × 5	25

As shown above {1, 4, 9, 16, 25},etc. are the perfect square.

Note: 4 is a Perfect Square

Now, To find the root of the non-negative number, We usually use these methods,

1. Check whether the number is perfect square or not By Guess and Check Method
2. Long Division Method
3. Prime Factorization Method

Now, let’s learn about these method in detail

Square Root of 4 by Guess and Check Method

In the Guess and Check method, we generally make a initial guess and then think it wisely and try to refine to get a number that is bit closer to the actual value.

Step 1: Begin by making an initial guess for the square root of the given number. As this depends on your understanding on perfect squares.

Step 2: Square your first guess, then multiply that number and check whether you find you number or not, If not then U need to move to next step. Either you got your answer.

Step 3: If the result is too large, then you choose a large number you should think less than that number vice versa.

Step 4: We need to repeat your process until you get your original number.

Step 5: Once you got your special number for the original number, then you should check by multiplying by itself. Once you confirm, You should think you had done a perfect approximation.

Now, Lets apply these steps for finding Square root of 4,

Step 1: Let’s start with the guess √4 = 2.

Step 2: check whether when we multiply by itself it gives original number or not as 2 × 2 = 4, so I got my original number.

Step 3: So, We got square root of 4 by Guess and Check Method.

Square Root of 4 by Long Division Method

Step 1: Group digits in pairs from the decimal point (if any) to the left and right.

Step 2: Find a number which is more suitable for the division or the number Whose Square is Less Than or Equal to the Original number.

Step 3: Subtract the perfect square from the first group of digits.

Step 4: Write down the next pair of digits.

Step 5: Double the current answer and find a digit to place next to it that, when multiplied by the new number, is less than or equal to the current number.

Step 6: Repeat steps 4-6 until desired accuracy is reached.

As We discussed earlier, 4 is a perfect square, So we get easily the square root by Long Division Method, Let’s Discuss how we find it.

To Find Square root of 4, we need to follow the steps

Step 1: We must first write 4 as 4.000000 to make it easier to divide.

Step 2: Now, Check whether 4 is perfect square or not, and we find yes 4 is a perfect square.

Step 3: If we found the perfect square, then simply get your answer as the square root of the number.

Note: It is easier to compute the square root of a perfect square number. if we talk about non-perfect square number then we need to perform long-division method step by step further. As 2 is not a perfect square So, To find the square root by long division method, please refer to square root of 2.

Learn, Square Root by Long Division Method

Square Root 4 by Prime Factorization Method

In this method, we normally perform the prime facorization method. If we get a pair of every number, then we must say that number is a perfect square.

For a Perfect Square

Suppose, The number 16, if we talk about their Prime factors, We got {2, 2, 2, 2} as their prime factor. As we noticed every number has an Identical pair then, we must say 16 is a perfect square and then We need to multiply the one element of every pair to find the square root of the 16. Like, we got 2 pairs here {(2 , 2) , (2 , 2)} then we need to multiply one element of every pair. So [2×2=4], 4 is the Square root of 16.

For a Non-Perfect Square

If we find any number which is not a perfect square, then You need to perform similar process, We need to find their prime factors, then we must find a non pair number, like if we talk about 12, we got {2, 2, 3} as their prime factors. We get a non-pair element.

As we understand we may write any number X as √X × √X. So make a pair of any single number like this.

Prime factors pairs for 12 is {(2 × 2),(√3 × √3)}.

So Square root of 12 is (2 ×√3).

Prime Factorization of 4

Now discuss the example,

Prime Factorization of 4

As we know, 4 is a perfect square.

So, If we talk about their prime factors, We get {2 , 2}. As we write 4 as 2 × 2 so that we get 4.

√4 = 2

So, Square root of 4 is 2.

Square Root of 4 – FAQs

What is the Square Root of 4?

The square root of 4 is 2

Is 4 is Perfect Square or not?

Yes, 4 is Perfect Square.

Is Square Root of 4 Always 2?

Yes, square root of 4 is always 2.

Is Square Root of 4 Rational or Irrational?

Value of square root of 4 is 2 and hence it is a rational number.