310 LearnersLast updated on May 26th, 2025
Square Root of 120
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
The different ways to find the square root of a number are prime factorization, long division and approximation/estimation method
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.
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:
Mistake 1
Trying to guess the square root instead of using the methods
Finding square roots for non-perfect squares without using the method is time-consuming. Always use the long division method to find the square root of non-perfect squares. Using the long-division method, we can find √120 as 10.954.
Mistake 2
Misunderstanding the square root of 120 with the division
A kid might divide 120 by 2, assuming that the result will give the square root. Understand the difference between finding a square root and dividing a number. A square root is the number that gets multiplied two times.
Mistake 3
Calculation mistake in subtracting the digits
Always be sure that you have checked the arithmetic calculations. If you subtract the digits incorrectly, the square root you get will also be incorrect.
Solved Questions on the Square Root of 120
Problem 1
Find the value of (√120)⁴
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
Problem 2
Calculate the perimeter of the square having an area of 120 square units
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
Problem 3
What is the value of √119 and √120 when added together?
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
Problem 4
If x = √120, what is the value of x²?
The value of x2 = 120
Explanation
When the square root gets squared, the root gets canceled. Here, x = √120 and x2 = (√120)2 = 120.
FAQs on 120 Square Root
1.Why is 120 not a perfect square?
2.What number is closest to √120?
3.Is √120 irrational?
4.What is √120 simplified?
5.What is the cube root of 120?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 120?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 120?
9.Does learning Algebra support future career opportunities for students in United States?
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
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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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