# Square Root of 120

Every non-negative real number has a unique non-negative square root, called the principal square root. Which is denoted by √x, where √ is called the radical sign or radix and the number under the radical sign here x is called the radicand.For example, the principal square root of 9 is 3, denoted by √9 = 3, because 32 = 3 x 3 = 9 and 3 is non-negative. The square root of 120 is that number which when multiplied by itself gives the number  120.

Number 120 is not a perfect square hence the square root of 120 results in a decimal number not the whole number.

Square Root of 120 ($\sqrt{120}$) = 10.954

### Square Root of 120

The square root of the rational number, 120 gives a decimal number and not a whole number, because the number 120 doesn’t have proper factors. Every non-negative real number has a non-negative square root, which is called the principal square root. Therefore, the square root of 120 gives a result as a unique non-negative number. It is denoted as √120, where √ is called radical sign or radix and the number 120, whose square root has to be derived is called radicand

### How to Calculate Square Root of 120

Calculating the square root of an imperfect square is a bit of a complex task. Following are the methods that can be used to find the square root of a number.

• Prime factorization method

• Repeated subtraction method

• Long division method

• Number line method

• Average method

This method works if the number is a perfect square, but, if the number is not a perfect square prime factorization method and the repeated subtraction method will not work, we have to use other methods for finding the square roots.

1. How to Find Square Root by Repeated Subtraction?

Answer : We know that by the property of square numbers, if a natural number is a square number, then it has to be the sum of successive odd numbers starting from 1. We will be using this property to find out the square root of a number by repeated subtraction method.Therefore, you can find the square root of a number by repeatedly subtracting successive odd numbers from the given square number, till you get zero.

For Example :  how to find the square root of 81 by repeated subtraction method.

1. 81 - 1 = 80

2. 80 - 3 = 77

3. 77 - 5 = 72

4. 72 - 7 = 65

5. 65 - 9 = 56

6. 56 - 11 = 45

7. 45 - 13 = 32

8. 32 - 15 = 17

9. 17 - 17 = 0

Here we got the result 0 in the 9th step, so the square root of 81 is 9 i.e   √81 = 9.

2. What is the Opposite of Square Root?

Answer: The square root of a number, is that number which when multiplied by itself gives the number itself. That number is called a perfect square. We calculate the area of a square as a product of side i.e side2, but if we have to calculate the side of a square we need to take the square root of the area. Thus we can say that the square root is the inverse operation of squaring a number. Hence square of a number is the opposite of square root of a number.

For Example : square root of 100 is 10 while the square of 10 is 100.