Square Root of 120

In this mini-lesson, we will calculate the square root of 120 by the long division method along with solved examples and interactive questions. The square root of a number is the number that gets multiplied to itself to give the original number. 4 is a square root of 16 because 4 × 4 = 16 and the symbol square root is written as √ and is an integral part of mathematics.
Let us take a look at what the square root of 120 is.

• Square Root of 120: √120 = 10.954
• Square of 120: 120² = 14400

What Is the Square Root of 120?

The square root is an inverse mathematical operation of a square. The square root of a number is the number that gets multiplied to itself to give the product. The square root of 120 is represented as √120. The square root of 120 in the exponent form is expressed as 120^1/2. The square root of 120 rounded to 3 decimal places is 10.954

Is the Square Root of 120 Rational or Irrational?

A rational number is a number that is of the form p/q where:

• p and q are integers
• q is not equal to 0

A number that cannot be expressed as a ratio of two integers is an irrational number. Non-terminating decimals having repeated numbers after the decimal point are rational numbers. Now let us look at the square root of 120.The decimal representation is: √120 = 10.9544511501. Do you think the decimal part stops after 10.9544511501? No, it is never-ending therefore it is a non-terminating decimal with non-repeating numbers. The number 10.9544511501.. can't be written in p/q form. So √120 is an irrational number.

How to Find the Square Root of 120?

Square Root of 120 can be calculated using various methods:

• By simplifying the radical of the numbers that are perfect squares.
• By long division method for perfect and non-perfect squares

Simplified Radical Form of Square Root of 120

To simplify the square root of 120, let us first express 120 as a product of its prime factors. Thus the prime factorization of 120 is: 2 × 2 × 2 × 3 × 5. To find the square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them. 
120 =  2 × 2 × 2 × 3 × 5
√120 = √(2 × 2 × 2 × 3 × 5)
= 2 × √(2 × 3 × 5)
=  2√30
Thus we have expressed the square root of 120 in the simplest radical form as 2√30
So, √120 = 2√30. The value of the square root of 11 by long division method consists of the following steps:

• Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
• Step 2:  Now, we find a number such that the square of any number gives a product less than or equal to the first pair. Here, the first pair just consists of 1 number, i.e. 1. Square of 1 gives product 1. The number is subtracted from the first pair and subsequently, the next pair is added as the divisor, i.e. 20
• Step 3: Now we take the double of quotient and place a digit with divisor along with its placement in the quotient, such that the new divisor, when multiplied with the individual number in the quotient, gives the product less than the dividend, subsequently subtracting it from the dividend.
• Step 4: For the new dividend obtained, we take the double of quotient and place a digit with divisor along with its placement in the quotient, such that the new divisor when multiplied with the individual number in quotient gives the product less than the dividend.
• Step 5: The difference is obtained in the above step. The double of the quotient is again taken and used as a divisor along with the involvement of one more digit such that the same digit is mentioned in the quotient resulting in a product less than the new divisor. 
• Step 6: The process is repeated the same way.

Therefore, the division is shown as:

Explore Square roots using illustrations and interactive examples

• Square Root of 25
• Square Root of 100
• Square Root of 121
• Square Root of 225
• Square Root of 45

Important Notes:

• The prime factorization method is used to write a square root of a non-perfect square number in the simplest radical form.
  For example: 45 = 3 × 3 × 5 = 3² × 35
• Irrational numbers cannot be expressed as a ratio of two integers. Example: pi, √2
• The square root of 120 in the radical form is expressed as 2√30

Challenging Questions:

• Can you think of any quadratic equation which has a root as √120?
• Is √-120 a real number?

FAQs On Square Root of 120

What is the square root of 120?

The square root of 120 is 4.6904

Why is √120 an irrational number?

A number with decimal expansion as non-terminating and non-repeating is always an irrational number. So, √120 is an irrational number.

Is the square root of 120 infinite?

The decimal expansion of √120 is infinite because it is non-terminating and non-repeating.

Is the square root of 120 an irrational number?

Yes, the square root of 120 is an irrational number.

Is square root of 120 a real number?

Yes, the square root of 120 is a real number.