Square Root of 120

Square root of 120 is ± 10.954. Here, 10.954 is the number which when multiplied by itself will give the product equal to 120. In radical form, it is written as √120. To find the square root of 120, we have to use the methods like long division method, the Prime Factorisation method, and the Repeated Subtraction Method.

Square Root Definition

A number’s square root is the value that gives the original number when multiplied by itself.

In the language of mathematics, the square root of a non-negative real number n is represented by the symbol n, and it fulfills the formula √(n​²) = n.

For example: The square root of 9 is 3, because 3 × 3 = 9.

What is the Square Root of 120?

The square root of 120 is 10.954. Whereas, Inverse operations include finding a number’s square and square root. To find the number’s square, you must multiply the number by itself. As 10.954 × 10.954 will give the square root of 120 and Even, the square root of numbers can be paired with positive numbers or negative numbers as well.

Let’s derive it:

The square root of 120 = √(2 × 2 × 2 × 3 × 5)
√120 = 2 √(2 × 3 × 5)
√120 = 2√30.

Now, for finding the accurate value we have to find the value of √30. Hence, √30 = 5.477
√120 = 2 × 5.477 (Multiplying √30 value with 2)
√120 = 10.9544

Therefore, the value of the Square Root of 120 is 10.9544.

How to Calculate a Square Root of 120?

Some of the methods are given below to find out the square root of 120.

• Prime Factorization Method
• Repeated Subtraction Method (estimation method)
• Long Division Method

Square Root 120 by Prime Factorization Method

Let’s derive the square root of 120 in the following steps by using the prime factorization method;

Step 1: Break down the prime Factorization of 120,

Thus, 120 = 2 × 2 × 2 × 3 × 5

Step 2: Now, we pair up the prime factors of identical numbers i.e.; (2 × 2) × 2 × 3 × 5.

Step 3: After that, Take a number from each pair and multiply it to get a square root. √120= √(2 × 2) × 2 × 3 × 5 or

√120 =2√30.

Step 4: Therefore, the square root of 120 is 2√30

As √30 = 5.477, thus square root of 120 is 2 × 5.477 = 10.9544.

Square Root 120 by Repeated Subtraction Method

The square root can be found by repeatedly subtracting odd numbers from the provided number until it equals zero. This process is known as repeated subtraction. So, In this process number of odd numbers we subtract here will be treated as a square root of 120.

• 120 – 1 = 119
• 119 – 3 = 116
• 116 – 5 = 111
• 111 – 7 = 104
• 104 – 9 = 95
• 95 – 11 = 84
• 84 – 13 = 71
• 71 – 15 = 56
• 56 – 17 = 39
• 39 – 19 = 20
• 20 – 21 = -1

So, here we have subtracted 11 odd numbers till now and past the zero and get the number in negative integer.

Therefore, The square root of 120 can be approximately near to 11.

Square root of 120 by Long division Method

The following procedures must be followed to determine the square root of 120:

Step 1: As here we start with the number 120 and use decimal points with the pairing of zeroes.

Step 2: Choose a perfect square less than 120 as the initial dividend. Hence divisor will be 10.

Step 3: Since the divisor is 10, the quotient is 10. therefore dividend will be 20. Subtract 100 from 120 and add 0 in the divisor.

Step 4: The new divisor is 209, the dividend is 20. Now put decimal after in quotient and bring down two zeros. Therefore the new dividend is 2000.

Step 5: Add a digit at the left of 1 in the divisor i.e. at the unit place and also place the same digit in the quotient such that the product is near to 2000.

Step 6: Multiply the new divisor 101 by the digit we just added to the quotient (1). This gives us 101 × 1 = 101. Subtract 2000 from 101 and get 1899.

Step 7: This process should be repeated until the square root of 120 is found in three decimal places or approximate value until 10. 95.

Is Square Root of 120 Rational or Irrational?

A real number that cannot be represented as a fraction of two integers is said to be irrational. The square root of 120 is irrational since it cannot be reduced to a fraction of two integers. As a result, 120 squared is an irrational number.

Square Root of 100 Value – FAQs

What is the Square Root Value of 120?

Value of square root of 120 is 10.954.

What is a Square of 120?

The square of 120 can be written as 120 × 120=14400.

What is the Symbol for the Square Root?

Symbol for square root is √.

Is 120 a Perfect Square?

No, 120 is not a perfect square because it can’t be expressed as the square of an integer

How can I Calculate the Square Root of 120?

The square root of 120 can be calculated manually using methods such as;

• Prime Factorization Method
• Repeated subtraction method
• Long division method