Everything About Square Root

The square root by its name can give some hints about what it is related to. Square is the process related to the multiplication of a single number again to the same number to obtain a different number. The root is the opposite of squaring. We multiply the number with itself to find the square of that number, however, to find the root of any number is the opposite process, we reverse the process to find the number that is the root of the number. We will learn both these mathematical terms in depth later in this article. The square root is a vital method that is involved in a majority of mathematics problems now and then. You’ll be aware of how to find square root? and even answer basic questions like what is the square root of 4?

What Is Square Root?

The square root is a combined method made from two different methods one is square and the other is root. Square is the process related to the multiplication of a single number again to the same number to obtain a different number. The root is the opposite of squaring. We multiply the number with itself to find the square of that number, however, to find the root of any number is the opposite process, we reverse the process to find the number that is the root of the number.

To understand better, 

The Square of the number 6 means, if we multiply 6 by another 6, then the number we will get is called the square value of 6.

6 * 6 = 36. 

Hence, we can say that 36 is the square value of a number called 6.

One thing you should notice here is that the square value of any number is always going to be a positive number.

Similarly, every number comprises two square roots. To understand  better,

The square root of the number 36 means that we have to find a number that has been multiplied twice to get 36. From the above example, we can clearly notice that 6 is the number because of which we received 36 when we squared.

Hence, we can say that 6 is the square root value of 36.

Square Root Definition

The square root of a number is calculated for a number (let’s say a) when we keep a as the base number and put (½) as the exponential degree on the base number which is 2 here.

Square root of a = (a)½  

A square root can also be elaborated in a very unique way like this. A square root is an identity that is not a number because it is [√_], but when this identity is multiplied with the same identity, it gives out a number as its multiplication product.

For example, √3 * √3 = 3.

How to Find Square Root?

Finding the square root of any number becomes extra easy if that number is a perfect square. A perfect square is only subjected to those numbers that can be expressed in the format of a base number with the degree 2. 

For example, for A to be a perfect square, there should exist a number B, that can be written as

A = (B)², where B has to be an integer.

There are broadly four methods for calculating the square root of any number.

• Square Root by Repeated Subtraction
• Square Root by Prime Factorization

Both of these methods are prominently used to derive square roots for perfect squares.

Square Root by Repeated Subtraction: This is the easiest method to find square root you can come across. Subtracting consecutive odd positive integer from the given number until the result of the difference comes out to be zero.

For example, let’s find out the square root value for 25.

25 – 1 = 24

24 – 3 = 21

21 – 5 = 16

16 – 7= 11

11 – 9 =2

Now, it is not possible to subtract any odd number like 11 from 2. Hence, we will stop here and then count the number of repetitive subtraction was required, i.e.5 in this case.

Therefore, the square root value of 25 is 5.

Square Root by Prime Factorization: This method involves the representation of the number for which the square root has to be calculated as a product of two or more two prime numbers.

Step1. Break the number into its prime factors and arrange them in the form of multiplication.

Step2. Arrange the prime factors such that the same factors form a pair.

Step3. Taking out one of two same factors from the pairs.

Step4. Multiply the unique separate prime factors with each other. The final product is the square root value of the respective number.

Let us calculate the square root of 64 by the prime factorization method.

64 = 2 * 2 * 2 * 2 * 2 * 2;

Now, we will form pairs.

64 = (2 * 2) * (2 * 2) * (2 * 2);

Selecting one of the 2 from the pairs.

64 = 2 * 2 * 2;

64 = (2)³

Hence, we found that 23 is the square root of 64 i.e. 8.

Conclusion

The square root is a combined method made from two different methods one is square and the other is root. Square is the process related to the multiplication of a single number again to the same number to obtain a different number. The root is the opposite of squaring. We multiply the number with itself to find the square of that number, however, to find the root of any number is the opposite process, we reverse the process to find the number that is the root of the number.