Square Root of 120
2026-02-28 17:54 Diff
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Last updated on August 5, 2025

The square root is the number obtained when a number is multiplied with itself. We apply the concept of square root in architecture, to measure volume and surface area. In this article, we’ll learn how to find the square root of 120.

What is the Square Root of 120

The square root of 120 is 10.954. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 120 is written as √120. 
 

Finding the square root of 120

Square root of 120 using prime Factorization Method

The prime factorization of 120 breaks 120 into its prime numbers. 


The numbers 2, 3, and 5 are the prime numbers .


Prime factorization of 120 is 23 × 31× 51.


Since 2 is repeating, we should pair them. We can’t pair 3 and 5 because they are not repeating.


Therefore, √20 is expressed as 2x√2 x √3 x√5, the simplest radical form.

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Square root of 120 using long division method

The long division method finds the square root of non-perfect squares.


The long division method finds the square root of non-perfect squares.


Step 1: Write down the number 120


Step 2:  Number 120 is a three-digit number, so pair them as (1), (20)


Step 3: Find the largest that is closest to the first pair (1), which is 12


Step 4: Write down 1 as the quotient, which will be the first digit of the square root.


Step 5: Subtracting 12  from 1 will leave zero as the remainder. Now bring down the second pair (20) and place it beside 0.


Step 6: Now double the quotient you have, that is multiply the quotient 1 with 2 and the result will be 2


Step 7: Choose a number such that it can be placed after 2. The two-digit number created should be less than the second pair (20). Here, we place 0 after 2, because the number formed will be greater than 20.


Step 8: Subtract 0 from 20  → 20-0 =20. Now add a decimal point after the new quotient and adding two zeros will make it 2000


Step 9: Apply step 7 over here and continue the process until you reach 0.


Step 10: We can write  √120 as 10.954
 

Square root of 120 by Approximation method

The approximation method finds the estimated square root of non-perfect squares.

Step 1: Identify the closest perfect square to 120. Numbers 100 and 121 are the closest perfect square to 120.


Step 2: We know that  √100 = 10 and  √121 = 11. Thus, we can say that  √120 lies between  10 and 11.


Step 3: Check if  √120 is closer to 10 or 11. Let us take 10.5 and 11. Since (10.5)2 is 110.25 and (11)2 is 121,  √120 lies between them.


Step 4: We can keep changing the values of 10.5 to 10. 6 and iterate the same process without changing 12 as the closest perfect square root.

The result of  √120 will be 10.954
 

Common Mistakes and How to Avoid Them in Square Root of 120

Take a look at mistakes a child can make while finding the square root of 120:

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Problem 1

Find the value of (√120)⁴

Okay, lets begin

Value of (√120)4 = 14115.8
 

Explanation

(√120)4 =  √120 x  √120 x  √120 x  √120 = 10.9 × 10.9 × 10.9 × 10.9 = 14115.8
 

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Problem 2

Calculate the perimeter of the square having an area of 120 square units

Okay, lets begin

Perimeter of the square = 43.817
 

Explanation

Square has 4 sides. So, the length of each side is  √120. To find the perimeter of a square, multiply 4 with  √120 → 4 x  √120 = 43.817
 

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Problem 3

What is the value of √119 and √120 when added together?

Okay, lets begin

The sum of  √119 and  √120 is 21.862
 

Explanation

√119 is 10.908 and √120 is 10.954. So, adding  √119 and  √120 will give the sum of 21.862
 

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Problem 4

If x = √120, what is the value of x²?

Okay, lets begin

The value of x2 = 120
 

Explanation

When the square root gets squared, the root gets canceled. Here, x = √120 and x2 = (√120)2 = 120.
 

Well explained 👍

FAQs on 120 Square Root

1.Why is 120 not a perfect square?

120 is not a perfect square because no number is multiplied by that number itself to give 120 as the product.
 

2.What number is closest to √120?

The √120 is closer to √100 and √121. The values of √100 and √121 are 10 and 11 respectively.
 

3.Is √120 irrational?

4.What is √120 simplified?

√120 is simplified using the long division method. Using this method,  √120 simplified will be 10.954
 

5.What is the cube root of 120?

The cube root of 120 is 4.932
 

Important Glossaries for Square Root of 120

  • Perfect Square: Product obtained when the same number gets multiplied twice
  • Approximate Value: Value closer to the exact number
  • Prime Factorization: Breaking down the number into its prime factors.

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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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: He loves to play the quiz with kids through algebra to make kids love it.