## what is the square root of 4

## Answer is 2 and -2

Explanation: The square root of 4 is denoted by âˆš4, where symbol â€˜âˆšâ€™ 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 Â±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 âˆša. âˆš is called the radical symbol or radix and in this example, the principal square root of 25 is 5 which is denoted by âˆš25 = 5, because 52 = 5 â€¢ 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 âˆša. âˆš is called the radical symbol or radix and in this example, the principal square root of 4 is 2 which is denoted by âˆš4 = 2 because 22 = 2 â€¢ 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 = âˆš40 = âˆš4 x âˆš10 = 2 âˆš10

Since, âˆš10 = 3.162 [By long division method]

Hence, âˆš40 = 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,

âˆš400 = âˆš4 x âˆš100 = 2 x 10 = 20

Hence, 20 is the answer.

## Square root of first 30 natural numbers is as follows

N. âˆšN

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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