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190 LearnersLast updated on December 2nd, 2024
Square root of 116
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.
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
Square Root of 116 Examples
Problem 1
If a = √116, find the result for the equation a²- 10
Explanation
Problem 2
Simplify (√116 + √116) + √116
Explanation
Problem 3
Calculate (10.77/10 + 10.77/9)
Explanation
FAQs on square root of 116
1.What is a principal square root ?
2.How can I find the square root of 4?
3.Can you tell whether the square root of 116 is rational or irrational?
4.Write the perfect square which is nearer to 116
5.What is the value of √11 and check if it’s an irrational number
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
