Square Root of 130
2026-02-28 09:02 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-130

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Last updated on August 5, 2025

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 130.

What is the Square Root of 130

The square root of 130 is ±11.4018. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 130 is written as √130. 
 

Finding the square root of 130

Square root of 130 using prime Factorization Method

The prime factorization of 130 breaks 130 into its prime numbers. 


The numbers 2, 5 and 13 are the prime numbers 


Prime factorization of 130 is 2 × 5 × 13


Since 2, 5 and 13 are not repeating, we can’t pair them


Therefore, √119 is expressed as √2 x √5 x √13, the simplest radical form

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Square root of 130 using long division method

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


Step 1: Write down the number 130


Step 2: Number 130 is a three-digit number, so pair them as (1), (30)


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 (30) and place it beside 0.


Step 6: Now double the quotient you have, that is added 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 (30). Here, we number 1 after 2, because the number formed will be less than 30.


Step 8: Subtract 21 from 30 → 30-21 =9. Now add a decimal point after the new quotient and adding two zeros will make it 900


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


Step 10: We can write  √30 as 11.4017
 

Square root of 130 by Approximation method

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

Step 1: Identify the closest perfect square to 130. Numbers 121 and 144 are the closest perfect square to 130.


Step 2: We know that  √121 = 11 and  √144 = 12. Thus, we can say that √130 lies between  11 and 12.


Step 3: Check if  √130 is closer to 11 or 12. Let us take 11.5 and 12. Since (11.5)2 is 132.25 and (12)2 is 144,  √130 lies between them.


Step 4: We can keep changing the values of 11.5 to 11. 6 and iterate the same process without changing 12 as the closest perfect square root.

The result of  √130 will be 11.4017
 

Common Mistakes and How to Avoid Them in Square Root of 130

Take a look at mistakes a child can make while finding the square root of 130:
 

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Problem 1

Find the value of (√130/3)

Okay, lets begin

The value of (√130/3) is 3.8005
 

Explanation

Find the approximate value of √130, which is 11.4017. Divide the approximate value by 3 to get 3.8005 (11.4017 ÷ 3 = 3.8005)

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Problem 2

Calculate the difference between square root of 130 and square root of 81

Okay, lets begin

The difference is 2.4017
 

Explanation

The approximate value of the square root of 130 is ±11.4017 and the square root of 81 is ±9. Now subtract 9 from 11.4017 to get 2.4017

Well explained 👍

Problem 3

If b = √130, what is b² - 130?

Okay, lets begin

The value for b2 - 130 is 0
 

Explanation

We know that b = √130, now b2 =130. Therefore, b2 - 130 = 130-130 = 0.
 

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Problem 4

Write √520 in terms of √130

Okay, lets begin

√520 can be written in terms of √130 as 2√130
 

Explanation

√520 with the help of prime factorization is written as 23 × 5 × 13. To express it in terms of, √520 is written as 2√130

Well explained 👍

FAQs on 130 Square Root

1.Write down the prime factors of 130

The prime factors of 130 are 2, 5 and 13
 

2.Is 130 a prime number?

Number 130 is not a prime number because it has more than 2 factors. Numbers with two factors are prime.
 

3.Is the square root of 130 a whole number?

The square root of 130 is not a whole number, but a decimal number
 

4.Where is root 130 situated?

The root 130 is situated between √121 and √144. The estimated value of √130 is 11.4017.

5.What is the difference between perfect square root and non-perfect square root?

The perfect square roots are whole numbers, while non-perfect squares are decimals.
 

Important Glossaries for Square Root of 130

  • 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.

Fun Fact

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