A Guide on Square Roots

A square root of a number is the number itself raised to the power of 2. To be more precise, the square of a number is when we multiply it by itself to give a different but original number. We denote the square root by the symbol √. 

Square and square roots are inversely related. For example, when we multiply a number by itself, we get its square. When raised to the power of ½, this square gives the original number again. For example, the square root of 9 is 3, and the square of 3 is 9.

Square Root Properties and Formula

As mentioned above, finding the square root of the number is the counter operation of finding the square of a number. The square of a number is when we multiply a number by itself. 

The square root of a number is when we factorise it, pair the factors, and find a common number. When we multiply this common number by itself would give the number whose square root we must determine.

In this concept, the squares always have an exponent of 2, and the square roots have a radical of 2. We denote the square root by a symbol called the radical. The number of which we find the square root is the radicand. The radicand is always under the square root symbol.

The square root of a number is the ½ power of that particular number. Squares and square roots are the special exponents and the inverse operations of each other. For example, if 9 is the number given, its square root will be 3, as 3 * 3 = 9, and the square of 3 will be 9.

There are some numbers whose square roots are easy to find, as they are the squares of a whole number in the number line. Such numbers are called perfect squares. These numbers are positive and are a product of themself. We can express these same numbers in powers of 2, and we can find their square roots by a power of 12. 

Methods to Find Square Roots

There are three methods by which we can find the square root of a number. They are as follows:

1. The Repeated Subtraction Method 

It is the simplest method to find a square root of a number. 

In this method, to find the square root, we will have to subtract the infrequent non-even numbers from the number whose square root we need to determine. We continue this subtraction until we obtain zero.

The only drawback of this method is that we can only use it when we have to find the square root of a perfect square number. 

Here, we can see how we use the repeated subtraction method to find the square root of 16.

16 – 1 = 15

15 – 3 = 12

12 – 5 = 7

7 – 7 = 0

We can observe that we have to do the subtraction four times to get the 0. Thus, we can see that the square root of this number is 4.

1. The Prime Factorisation Method

In this method, we can represent the given number as the product of two prime numbers. We then form pairs of similar factors of the number such that both the factors in a pair are equal. 

We take one of these pairs and calculate their product. The number obtained number is the square root of the given number.

1. The Estimation Method

It is a method in which we use the concept of estimation and approximation to make a reasonable guess to calculate the square root of the given number. This method is handy. We find the perfect square closer to the given number. 

For example, if we have to find the square root of 15, the perfect squares nearest to 15 are 16 and 9. The former is a square of 4, and the latter is a square of 3. So, the square root of 15 is a number that lies between 3 and 4. 

Let us find the squares of the numbers 3.8 and 3.9. Now, 

3.82 = 14.44 

3.92 = 15.21. 

Therefore, the square root of 15 lies somewhere between 3.8 and 3.9.

Conclusion

In this article, we learned about the different methods of finding the square root of a number. We commonly use these methods in day to day calculations. All of them tend to give the most accurate answer possible. 

We learned how the repeated subtraction number lets us subtract the infrequent non-even numbers and helps us find the square root. However, this method is inappropriate for bigger numbers as it would become lengthy. 

Then we learned about a more convenient and precise way of the prime factorisation method. Here, we use the number’s prime factors to find its square root. 

We also learned about the estimation and approximation method that comes in handy when we don’t have a perfect square or want the answer in decimals.