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Last updated on May 26th, 2025

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Square Root of 109

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When we multiply a number by itself, we get a number, the number which is multiplied is called the square root. It is a very important and interesting part of mathematics. You must have applied it for measuring each side of a square from the total area.

Square Root of 109 for Vietnamese Students
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What is the Square Root of 109?

When we multiply a number by itself we get a number, that number is the square root of 109. The square root of 109 is an irrational number. As we cannot write the number in the form of a ratio. It is denoted by 109 and is approximately equal to 10.4403. 


Exponential form : 1091/2  ≅ 10.4403. 


Radical Form:√109 

10

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Finding the Square Root of 109


We can find the square root of a number by using methods like: Prime Factorization; Long Division method; Approximation method and Subtraction method.
 

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Prime Factorization

The breaking down of a number into smaller numbers is prime factorization. Here, 109 is a prime number, it cannot be broken down into smaller numbers other than 1 and 109. So, from this method we cannot find the exact square root, but we confirm that 109 is not a perfect square.
 

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Long Division Method

In this method, we get to find the value of the square root precisely.

 

Grouping the digits: We start with pairing the digits from the decimal part 109.00


Find the number whose square will be less than or equal to 109 i.e., 10 (since 102 = 100).


Subtract 102 = 100 from 109, which leaves us with 9.


Now we bring down two zeros, which makes it 900


Next double the divisor 10, we get 20. Next we find the largest digit which will be lesser than or equal to 900.


Repeat the steps to get the next decimal places.


So after calculation we get, √109  = 10.4403.

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Approximation Method

As 102 =100 and 112 =121, the square root of 109 lies between 10 and 11.


Start by guessing 10.4 which is nearest to 10.


10.42 = 108.16 which is too less, keep repeating till we reach the nearest number


Go to the next number 10.4403, 10.44032 = 109 which is close.


So, √109  = 10.4403

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Subtraction Method

The subtraction method includes subtracting consecutive odd numbers from 109 to see how many steps we need to reach zero. However, since 109 is not a perfect square, we cannot exactly reach 0. 

 

109 -1 =108


108-3=105


105-5=100


100-7=93


93-9=84


84 -11 =73


73-13=60


60-15=45


45-17=28


28-19=9


9-21=-12

 

As we did not get zero, we understand that 109 is not a perfect square.

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Common Mistakes and How to Avoid Them in the Square Root of 109

While learning about square roots, students may likely make mistakes, to avoid them a few mistakes with solutions are given below:
 

Mistake 1

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 Thinking 109 is a perfect square
 

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Few students think mistakenly that 109 is a perfect square, as it lies between 100 and 121. They should not rely on assuming the squares of the numbers, instead children should practice square roots of numbers and apply the methods to find square roots.
 

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Square Root of 109 Examples

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Problem 1

If, x = 10.4403, find the value of x.

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 If square root of   x = 10.4403,

 
Then, 


x= (10.4403)2 
 

Explanation

Here, the root when shifted to the RHS it becomes the squared power of the number


x=10.4403 × 10.4403


x=109.


So the value of x is 109.
 

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Problem 2

Solve for x if x+5 = 6.

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 x+5 = 6


x+5=62 
 

Explanation

Here, the root when shifted to the RHS it becomes the squared power of the number


x+5=36


x=36-5


x=31.


So the value of x is 31
 

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Problem 3

Find the value of 109 +25 .

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109 +25 .

 
First we find the root of each number, which will be,


109 =10.4403


25 =5
 

Explanation

Now, we add the roots of both the numbers


10.4403 + 5 =15.4403


We get, 15.4403
 

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Problem 4

Solve: 10/√109

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 To simplify, 10/√109  We multiply the number in the denominator with the numerator and the denominator, which is called rationalizing. 

Explanation

10/√109  x  √109/ √109  = 10√109 /√109  , here when two square roots with the same number are multiplied the roots get canceled (in the denominator), and we are left with the same number, hence √109x √109  = 109.
After rationalizing, we get,  10√109 /√109 

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FAQs on 109 Square Root

1.How to write the simplified square root form of 109?

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2.Is 109 a perfect Square or not ?

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3.What number is the cube of 109?

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4.What is the simplest form of root of 108?

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5.How does learning Algebra help students in Vietnam make better decisions in daily life?

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6.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 109?

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7.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 109?

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8.Does learning Algebra support future career opportunities for students in Vietnam?

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Important Glossaries for Square Root of 109

  • Exponent form: Writing the square root of a number in the form of degree or powers. For example, 1091/2  ≅ 4.7958

 

  • Approximation method: It is the method in which we find a close but not an exact value of a number. For example, √109 =10.4403.
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About BrightChamps in Vietnam

At BrightChamps, we know algebra is more than symbols—it’s a path to countless opportunities! Our goal is to help children across Vietnam grasp essential math skills, with today’s focus on the Square Root of 109 and a special look at square roots—in an engaging, enjoyable, and easy-to-learn way. Whether your child is figuring out how fast a roller coaster moves at Suoi Tien Theme Park, keeping track of local football scores, or budgeting their allowance for new gadgets, mastering algebra gives them the confidence to handle daily challenges. Our interactive lessons make learning easy and fun. Since children in Vietnam learn in different ways, we adapt to each learner’s style. From Ho Chi Minh City’s vibrant streets to the beautiful Ha Long Bay, BrightChamps makes math come alive throughout Vietnam. Let’s make square roots an exciting part of every child’s math adventure!
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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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Fun Fact

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

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