356 LearnersLast updated on May 26th, 2025
Square Root of 109
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.
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.
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.
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.
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
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.
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
Thinking 109 is a perfect square
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.
Mistake 2
Rounding off the square root too soon.
Children should not stop the long division just after one or two decimal points, which leads to improper results, as they round off the square too early. To avoid this, they should practice division till they reach the desired solution.
Mistake 3
Confusing the square root with the square of the number.
Students sometimes think square root as square of a number and get confused, instead of finding the square root they double the number. To avoid this, children should practice finding square roots of numbers
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Square Root of 109 Examples
Problem 1
If, x = 10.4403, find the value of x.
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.
Problem 2
Solve for x if x+5 = 6.
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
Problem 3
Find the value of 109 +25 .
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
Problem 4
Solve: 10/√109
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?
2.Is 109 a perfect Square or not ?
3.What number is the cube of 109?
4.What is the simplest form of root of 108?
5.How does learning Algebra help students in Vietnam make better decisions in daily life?
6.How can cultural or local activities in Vietnam support learning Algebra topics such as Square Root of 109?
7.How do technology and digital tools in Vietnam support learning Algebra and Square Root of 109?
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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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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