Square Root Of 4

The square root of 4 is denoted by √4, where symbol ‘√’ is the symbol of the square root. Number 4 is a perfect square. So it is easy to find the root of 4 and other such perfect numbers. Whereas in the case of non-perfect square number, to find its root value we have to use the long division method.

The value of root 4 is equal to exactly 2. But the  roots could be positive or negative or we can say there are always two roots for any given number. Hence, root 4 is equal to ±2 or +2 and -2 (positive 2 and negative 2). You can also find square root on a calculator. To calculate the square root of a number online click here Square root calculator.

Basically, a number when get multiplied by itself is called a square number. For example: 3 x 3 = 9 so 9 is a square number. You can see some more examples below:

  • 16 = 4 x 4 = 42
  • 64 = 8 x 8 = 82
  • 49 = 7 x 7 = 72
  • 36 = 6 x 6 = 62

In this article, we will learn to find the root of 4. This topic is widely explained in Class 8 syllabus, where square and the square root of different numbers have been determined. Let us see some basics related to square root.

Also, read:

What is a perfect square?

A simple way to know if a number is a perfect square or not:

  • If a number ends with 2, 3, 7 ,8 at unit place then it is not a perfect square
  • If a number ends with 1, 4, 5, 6, 9 in the unit place then it is definitely a perfect square

What is the Square root of 4?

In mathematics, squaring a number is not difficult as the calculation is easy. To find the square root of a number is complicated as we need to find the original number that was squared. Let us consider an example: +5 and -5 are square roots of 25 because 52 = (-5)2 = 25. A real number which is non-negative has a unique nonnegative square root. It is called principal square root denoted by √a. √ is called the radical symbol or radix and in this example, the principal square root of 25 is 5 which is denoted by √25 = 5, because 52 = 5 • 5 = 25 and 5 is nonnegative. The number underneath the radical symbol is called the radicand. Here the radicand is 25.

Considering the above example, +2 and -2 are square roots of 4 because 22 = (-2)2 = 4. A real number which is non negative has a unique nonnegative square root. It is called principal square root denoted by √a. √ is called the radical symbol or radix and in this example the principal square root of 4 is 2 which is denoted by √4 = 2, because 22 = 2 • 2 = 4 and 2 is nonnegative. The number underneath the radical symbol is called the radicand. Here the radicand is 4. Here is a video for the shortcut method to find out the square root of a number.

Square root of 40

40 is the multiple of 4 and 10. As we already know, the root of 4 is equal to 2 but what about number 10. Since, 10 is not a perfect square, thus we have to find the root of 10 using long division method.

Hence, we can write,

Value of root 40 = √40 = √4 x √10 = 2 √10

Since, √10 = 3.162    [By long division method]

Hence, √40 = 2 x 3.162 = 6.324

Square root of 400

When number 4 is multiplied by 100 it results in 400, such as;

4 x 100 = 400

As you can see, both 4 and 100 are the perfect squares. Hence, it is easy to find the root value of 400. Therefore,

√400 = √4 x √100 = 2 x 10 = 20

Hence, is the answer.

Square Root From 1 to 50

Here is the list of square root of numbers from 1 to 50. Student can use this table to do calculations.

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 3.464
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
26 5.099
27 5.196
28 5.292
29 5.385
30 5.477
31 5.568
32 5.657
33 5.745
34 5.831
35 5.916
36 6
37 6.083
38 6.164
39 6.245
40 6.325
41 6.403
42 6.481
43 6.557
44 6.633
45 6.708
46 6.782
47 6.856
48 6.928
49 7
50 7.071

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