Square root of 120 is the value which signifies the reverse of the square of a number. Basically, the square root of a number say â€˜nâ€™, is another number say â€˜mâ€™, in such a way that when m is multiplied to itself or when we take the square of m, it gives number â€˜nâ€™.

The square root of rational number, 120 gives a decimal number and not a whole number. It is because the number 120 doesnâ€™t have proper factors. Usually, by the method of prime factorization, we get the set of numbers which are multiplied together to get the initial number.

For all non-negative real numbers, we can find a unique non-negative square root, which is called the principal square root. Therefore, the square root of 120 gives us a unique non-negative number. It is denoted as âˆš120, where âˆš is called radical sign or radix. The number 120, whose square has to be derived is called as radicand. Or we can say the term or the number underneath of the radical sign is specified as radicand.

## Simplification of Square Root of 120

**The value of the square root of 120 is 10.954451150103.**Â Let us learn how to find out its value. As discussed, when a number is multiplied by itself, it gives a value whose square root can be taken. Like if write the square of a number equal to another b, we get,

b = a^{2}

Now if we have to take the square root of b, we get,

âˆšb = âˆša^{2}

So, the root cancels the square or un-square it. Therefore we get,

âˆšb = a

Similarly, we can find the square root of 120 here, by writing its prime factors first.

We can write,Â 120 = 2 Ã— 2 Ã— 2 Ã— 3 Ã— 5

Taking out the root means, taking out the pair of numbers present underneath the radix.

Therefore, the square root of 120, âˆš120 = \(\sqrt{2 * 2 * 2 * 3 * 5}\)

â‡’ âˆš120 = 2 \(\sqrt{2 * 3 * 5}\) = 2âˆš30

â‡’ âˆš120 = 2âˆš30.

This is the radical form of âˆš120. But to find the accurate value, we have to mention the value of âˆš30. The value of the square of 30 is 5.477. Therefore,

âˆš120 = 2 Ã— 5.477 = 10.9544

You can use square root long division method to find the value of âˆš30.Â This method gives the perfect value for any square root. Apart from these are we have certain methods by the means of which we can find the square root of a given number.

We can represent the square roots in a graphical form.

**Properties of square roots**

- The general form of representation of square root is âˆšx = a, where x has two roots +a and -a.
- The principal square root function can be represented as f(x) = âˆšx. It is used to map the area of the square to its side length.
- The square root of a perfect square gives non-fraction and non-decimal number.
- For all non-negative real numbers a and b,
- âˆšab = âˆša.âˆšb
- The square root of a non-negative real number x, can be represented as,
- âˆšx= x
^{1/2}

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