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209 LearnersLast updated on December 2nd, 2024
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
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
Square Root of 109 Examples
Problem 1
If, x = 10.4403, find the value of x.
Explanation
Problem 2
Solve for x if x+5 = 6.
Explanation
Problem 3
Find the value of 109 +25 .
Explanation
Problem 4
Solve: 10/√109
Explanation
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?
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
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.
