Square Root of 4

The square root of 4 is simply just 2 or in other words, \[\sqrt 4 \] = 2. It is one of those numbers which have a perfect square number. Since it is a perfect square number, the square root of 4 can be found easily. In Mathematics, the sq root of 4 is presented or written as \[\sqrt 4 \]. It is a positive number and also the value of \[\sqrt 4 \] when multiplied by itself, gives you composite number 4. In case the square root of the number isn’t the perfect one, the end result is going to be an irrational number. To separate itself from a negative number with similar properties, it is called as the principal root of 4. 


The exact value of \[\sqrt 4 \] is equal to 2. Now the roots of \[\sqrt 4 \] can either be positive or it can be negative. Or in other words, we can state that every number has two roots: positive and negative. Therefore, the value of \[\sqrt 4 \] can be either -2 or it can be + 2 or it can also be represented as ± 2. The square root of any number can be figured out using a calculator too.


When a number is multiplied by itself, it is said to be the square of the number. Here, the value of root 4 is exactly equal to 2. How can we prove this? By just multiplying 2 with 2 just like this - 2 x 2 = 4. Some similar examples are 4 x 4 = 16, 5 x 5 = 25, 6 x 6 = 36, etc.


In this section, you will be studying thoroughly about the square root of 4. You will be learning about the square and the square root of 4 and other different numbers. But before we go ahead, you will need to know about the basics of root 4.


What is the square root of 4?

The square of any number can be found out by simple multiplication methods. Now, to find the square root, you have to figure out the original number that had been multiplied by itself. For example: let’s consider +3 and -3 are the square roots of 9. Now, how do we know that? 3 x 3 = 9 or it can also be (-3)2 = (-3) x (-3) = 9. A real number that is positive has a positive root. It is denoted by the \[\sqrt x \], where x stands for the number whose square root is to be found and the value of x is called the radicand. The symbol √ is called the radix or it is also known as the radicle symbol. Now, the principal square root of 29 is 7 and this can be denoted by 72 = 7 x 7 = 49, and the number 7 is a non-negative number. Here, the radicand is 49.


Square Root of 40

The multiples of 40 are: 2 x 2 x 2 x 5. We can also say that the multiples of 40 are 10 and 4. The square root of four is equal to 2. Now we still have 10 left. Even though we know that 10 is not a perfect square, we can still find the root of 10 with the help of the long division method.  


Now, 


We know that, 


The square root of 40 =  \[\sqrt 40 \]

  =  \[\sqrt 4 \] x  \[\sqrt 10 \]

  =   2 x  \[\sqrt 10 \]

  =   2 x 3.162

  =   6.324


Square Root of 400

The multiples of 40 are 2 x 2 x 2 x 2 x 5 x 5. We can also say that the multiples of 400 are 10 and 4. The square root of four is equal to 2. Now we still have 100 left. Even 100 is a perfect square, the root of 100 = 10.


Now,


We know that, 


The square root of 400 =  \[\sqrt 400 \]

  =  \[\sqrt 4 \] x  \[\sqrt 100 \]

  =   2 x  10

  =   20



Square Root of 4000

The multiples of 4000 are: 2 x 2 x 10 x 10 x 10. We can also say that the multiples of 40 are 400 and 10. We know that the square root of 400 is 20. Now we still have 10 left. Even though we know that 10 is not a perfect square, we can still find the root of 10 with the help of the long division method.  


Now, 


We know that, 


The square root of 4000 =  \[\sqrt 4000 \]

  =  \[\sqrt 400 \] x  \[\sqrt 10 \]

  =   20 x  \[\sqrt 10 \]

  =   20 x 3.162

  =   63.24


Square Root From 1 to 25

Check the list given below to learn the square roots of the number from 1 to 25. 


Number

Square Root Value

1

1

2

1.414

3

1.732

4

2

5

2.236

6

2.449

7

2.646

8

2.828

9

3

10

3.162

11

3.317

12

3.463

13

3.606

14

3.742

15

3.873

16

4

17

4.123

18

4.243

19

4.359

20

4.472

21

4.583

22

4.69

23

4.796

24

4.899

25

5

FAQ (Frequently Asked Questions)

1. What is the square root of 4?

The exact value of √4 is equal to 2. Now the roots of √4 can either be positive or it can be negative. Or in other words, we can state that every number has two roots: positive and negative. Therefore, the value of √4 can be either -2 or it can be + 2 or it can also be represented as ± 2. The square root of any number can be figured out using a calculator too.

2.How to find the square root of 400?

The multiples of 40 are 2 x 2 x 2 x 2 x 5 x 5. We can also say that the multiples of 400 are 10 and 4. The square root of four is equal to 2. Now we still have 100 left. Even 100 is a perfect square, the root of 100 = 10.


Now,


We know that, 


The square root of 400 =  √400

    =  √4 x  √100

    =   2 x  10

              =   20