what is the square root of 4
Answer is 2 and -2
Explanation: 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).
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, you 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.
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 the unit place then it is not a perfect square
If a number is a perfect square, then it ends with 1, 4, 5, 6, 9 in the unit place but vice versa is not possible. For example, 25 is a perfect square, whereas 35 is not
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 non-negative real number has a unique non-negative 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 non-negative. 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 non-negative real number has a unique non-negative 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 are non-negative. 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 the 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, 20 is the answer.
Square root of first 30 natural numbers is as follows
N. √N
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
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