Square root of 116
2026-02-21 20:38 Diff
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Last updated on August 5, 2025

The square root of 116 can be ‘x’ where we get 116 as a result when ‘y’ gets multiplied by y itself → y × y. The number 116 has a special square root called the principal square root.

What is the square root of 116?

  ±10.77 is the square root of 116. To find the square root, we should use the inverse process of squaring a number. So, when 10.77 is squared, we get 116. The radical form of 116 is expressed as √116, where ‘√’ is the radical symbol. The square root of 116 is expressed in its exponential form as (116)½.

Finding the Square Root of 116

The square root of 116 can be calculated with the help of different methods such as:

  • Prime Factorization Method
  • Long Division Method
  • Approximation or Estimation Method
     

Square Root of 116 By Prime Factorization

The prime factorization of 116 is done by breaking 116 into its prime factors until the quotient can’t be divided anymore. 

The prime factors of 116 are 2 and 29, expressed as 2×2×29  → 22 × 29

If a number exists that cannot be paired, then that number is written using the radical sign along with paired numbers. Hence, 2√29 is the simplest form of √116.

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Square Root of 116 By Long division

The long division method is used to find the square root of non-perfect squares. This method involves dividing the dividend with divisors, which results in not just a quotient but also a remainder.

To calculate √116:

Step 1: Draw a horizontal above 116


Step 2: Now find the closest perfect square that lies near to 116. The perfect square closest to 116 is 100  → 102


Step 3: Divide 116 by 10. The quotient will remain 10 and the remainder will be 16 (116-100)


Step 4: Bring down the remainder 16 and add two zeros. Add a decimal point to the quotient, it turns to 10.0.

Step 5: Double the quotient and use it as the new divisor. Now pick a number that will complete the divisor so that when it is multiplied by, the product is less than or equal to 1600. 

Step 6: Continue to the division to find the √116

Square Root of 116 By Approximation

The approximation method estimates the square root by considering the closest perfect square.

Step 1: Nearest perfect square to 116 is √100=10 and √121=11


Step 2: 116 falls between 100 and 121 therefore the square root falls between 10 and 11


Step 3:  We find that  √116 = 10.77.
 

Common Mistakes and How to Avoid Them in square root of 116

some common mistakes with their solutions are given below:

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Problem 1

If a = √116, find the result for the equation a²- 10

Okay, lets begin

The result will be 106
 

Explanation

 It’s already given that a = √116. Therefore, a2 = 116.
According to the equation a2 - 10 → 116 - 10 = 106.
 

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Problem 2

Simplify (√116 + √116) + √116

Okay, lets begin

Solution: 126.7629
 

Explanation

√116 is 10. 77.

So (√116+√116) x √116 is (10.77+10.77)x10.77 is 126.7629
 

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Problem 3

Calculate (10.77/10 + 10.77/9)

Okay, lets begin

 The result will be 2.273
 

Explanation

10.77/10 gives 1.077 and 10,77/9 gives 1.196. So, (10.77/10 + 10.77/9) will give 2.273 as result.
 

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FAQs on square root of 116

1.What is a principal square root ?

The unique non-negative square root of a number is known as the principal square root. For example, √116 is the principal square root.
 

2.How can I find the square root of 4?

The square root of 4 can be found using methods like prime factorization and long division.
 

3.Can you tell whether the square root of 116 is rational or irrational?

The square root of 116 is ±10.77. So, 10.77 is an irrational number because it cannot be obtained dividing two integers.

4.Write the perfect square which is nearer to 116

The perfect square is100, having 10 as its square root. When 10 is multiplied two times, we get 100.
 

5.What is the value of √11 and check if it’s an irrational number

The value for √11 is 3.32, which is an irrational number. It is an irrational number because it cannot be obtained dividing two integers.
 

Important Glossaries for Square Root of 116

  • Prime number: Numbers having two factors.
  • Perfect square: Numbers whose square root include only whole numbers
  • Prime Factorization:  Process of expressing the product of prime numbers in exponential form.
  • Non-perfect square: Numbers whose square root contains decimals.
     

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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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