The square root of 4 is simply 2 or √4 = 2; the square root of 4 is easy to find since it is a perfect square number. It is a positive integer with the value √4. When multiplied by itself, it yields the composite number 4.
If the integer’s square root is not the perfect one, the outcome is an irrational number. To separate itself from a negative number with similar properties, it is called the principal root of 4.
- The precise value of √4 equals 2.
- Now, the roots of √4 might be either positive or negative. Or, to put it another way, every number has two roots: positive and negative.
- As a result, the value of √4 can be either -2 (Negative) or 2, or it can alternatively be represented as 2.
- A calculator may also be used to calculate the square root of any value.
When a number is multiplied by itself, the result is referred to as the number’s square.
The root 4 value is precisely equal to 2 in this case. How can we demonstrate this? Simply multiplying two by two, as in 2 x 2 = 4. Similar instances are 4 × 4 = 16, 10 x 10 = 100, 8 x 8 = 64, and so on.
In this section, we will study the facts about the square and square root 4, but before proceeding, we must be well versed with the concept of the square root of 4.
What is the root 4 value?
Simple multiplication algorithms may be used to calculate the square of any number. To obtain the square root, you must first determine the original integer that has been multiplied by itself.
For example, 4 and -4 (Negative) are the square roots of 16; how can this be concluded? , if we multiply 4 and 4, we will be getting 16 as the product. Similarly, if we multiple -4 with -4 again, we will get 16 as the product, proving what we have mentioned above.
A positive real number has a positive root.
- It is symbolised by the symbol √x, where x represents the integer whose square root must be calculated, and the value of x is known as the radicand.
- The sign is known as the radix. However, it can also be referred to as the radicle symbol.
For example, while calculating the square root of 81, the principal square root of the radicand is 9, which can also be illustrated as the square of 9 or 9 X 9 = 81, and the number 9 is a non-negative number. Also, the radicand in the example is 81.
Method of Calculating a square root with examples
Calculating the square root of 40
First of all, to determine the square root of a number, we must find out its multiples.
In the case of 40, the multiples can be illustrated as under:
The multiples 40 = 2 X 2 X 2 X 5, or it can be safely concluded that the multiples of 40 are 4 and 10. For 4, we know its square root is 2, and we are still left to calculate for 10. Even though we know that 10 is not a perfect square, we can still use the long division approach to discover the root of 10.
Now
It can be represented mathematically as follows:
The square root of 40 = √40
√40 = √4 X √10
= 2 X √10
= 2 X 3.162 ( Where √10 = 3.162)
= 6.324
Calculating the square root of 400
First of all, to determine the square root of a number, we must find out its multiples
In the case of 400, the multiples can be illustrated as under:
The multiples 400 = 2 X 2 X 2 X 2 X 5 X 5, or it can be safely concluded that the multiples of 400 are 4 and 100. For 4, we are aware that its square root is 2, and for 100, it is an easy peasy 10
Now
It can be represented mathematically as follows:
The square root of 400 = √400
√400 = √4 X √100
= 2 X √100
= 2 X 10 ( Where √100 =10)
= 20
Calculating the square root of 4000
First of all, to determine the square root of a number, we must find out its multiples.
In the case of 4000, the multiples can be illustrated as under:
The multiples 4000 = 2 X 2 X 2 X 2 X 2 X 5 X 5 X 5, or it can be safely concluded that the multiples of 4000 are 400 and 10. For 400, we know its square root is 20, and we are still left to calculate for 10. Even though we know that 10 is not a perfect square, we can still use the long division approach to discover the root of 10.
Now
It can be represented mathematically as follows:
The square root of 4000 = √4000
√4000 = √400 X √10
= 20 X √10
= 20 X 3.162 ( Where √10 = 3.162)
= 63.24
For a ready reference, a Table representing the value of square roots is illustrated below:
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 |
Solved Examples-
Question: What Is the value of the square root of 4?
Answer: The precise value of √4 is 2. Now, the roots of 4 might be either positive or negative. Or, to put it another way, every number has two roots: positive and negative. As a result, the value of 4 can be either -2 or 2, or it can alternatively be represented as 2. A calculator may also be used to calculate the square root of any value.
Question: How to find the square root of 900?
Answer: First of all, to determine the square root of a number, we must find out its multiples
In the case of 900, the multiples can be illustrated as under:
The multiples 900 = 3 X 3 X 2 X 2 X 5 X 5, or it can be safely concluded that the multiples of 400 are 9 and 100. For 9, we are aware that its square root is 3, and for 100, it is an easy peasy 10
Now
It can be represented mathematically as follows:
The square root of 900 = √900
√900 = √9 X √100
= 3 X √100
= 3 X 10 ( Where √100 =10)
= 30
Conclusion
Therefore, we hope from this article you know have a clear understanding of how to find the Square Root of 4. Apply a similar process for identifying the square root value of other numbers.