265 LearnersLast updated on May 26th, 2025
Square Root of 119
Square root is the number obtained when a number is multiplied with itself. We apply the concept of square root in architecture, to measure volume and surface area. In this article, we’ll learn how to find the square root of 119.
What is the Square Root of 119
The square root of 119 is 10.9087. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 119 is written as √119.
Finding the square root of 119
The different ways to find the square root of a number are prime factorization, long division and approximation/estimation method
Square root of 119 using prime Factorization Method
The prime factorization of 119 breaks 119 into its prime numbers.
The numbers 7 and 17 are the prime numbers
Prime factorization of 119 is 7 × 17
Since 7 and 17 are not repeating, we can’t pair them
Therefore, √119 is expressed as √7 x √17, the simplest radical form
Square root of 119 using long division method
The long division method finds the square root of non-perfect squares.
Step 1: Write down the number 119
Step 2: Number 119 is a three-digit number, so pair them as (1), (19)
Step 3: Find the largest that is closest to the first pair (1), which is 12
Step 4: Write down 1 as the quotient, which will be the first digit of the square root.
Step 5: Subtracting 12 from 1 will leave zero as the remainder. Now bring down the second pair (19) and place it beside 0.
Step 6: Now double the quotient you have, that is multiply the quotient 1 with 2 and the result will be 2
Step 7: Choose a number such that it can be placed after 2. The two-digit number created should be less than the second pair (19). Here, we can’t add any number after 2, because the number formed will be greater than 19.
Step 8: Subtract 19 from 2 → 19-2 =17. Now add a decimal point after the new quotient and adding two zeros will make it 1700
Step 9: Apply step 7 over here and continue the process until you reach 0.
Step 10: We can write √119 as 10.9087
Square root of 119 by Approximation method
The approximation method finds the estimated square root of non-perfect squares.
Step 1: Identify the closest perfect square to 119. Numbers 100 and 121 are the closest perfect square to 119.
Step 2: We know that √100 = 10 and √121 = 11. Thus, we can say that √119 lies between 10 and 11.
Step 3: Check if √119 is closer to 10 or 11. Let us take 10.5 and 11. Since (10.5)2 is 110.25 and (11)2 is 121, √119 lies between them.
Step 4: We can keep changing the values of 10.5 to 10. 6 and iterate the same process without changing 12 as the closest perfect square root.
The result of √119 will be 10.9087
Common Mistakes and How to Avoid Them in Square Root of 119
Take a look at mistakes a child can make while finding the square root of 119:
Mistake 1
Trying to guess the square root instead using the methods
Finding square root for non-perfect squares without using the method is time-consuming. Always use the long division method to find the square root of non-perfect squares. Using the long-division method, we can find √119 as 10.9087.
Square Root of 119 Examples
Problem 1
119 is not a perfect square. What are the perfect squares that are close to 119?
The closes perfect squares are 10 and 11
Explanation
A perfect square is the product of the same number multiplied two times. Here, 102 will give 100, and 112 will give 121 as the perfect square near to 119. The square root of 119 will fall between 10 and 11.
Problem 2
Is the square root of 119 closer to the square root of 100 or 121?
The square root of 119 is closer to the square root of 121.
Explanation
The approximate value for the square root of 119 is ±10.9087. The square root of 100 and 121 will be 10 and 11. So, the square root of 119 ±10.9087 is closer to 11.
Problem 3
What is √119 subtracted from 5?
Subtracting √119 from 5 will give 5.9087
Explanation
The estimated value of √119 is 10.9087. Now if we subtract 5 from 10.9087, we get 5.9087 as the result (10.9087-5 = 5.9087)
Problem 4
Question: If y = √119, find the value of 3y
The value of 3y is 32.7261
Explanation
The value of √119 is 10.9087. When 3 is multiplied by it, we get 32.7261 as the product(3y = 3 × 10.9087)
FAQs on 119 Square Root
1.Is 119 a perfect square?
2.What are the factors of 119?
3.Can you identify √119 as rational?
4.Where is √119 located?
5.What is the fourth root of 119?
6.How does learning Algebra help students in Canada make better decisions in daily life?
7.How can cultural or local activities in Canada support learning Algebra topics such as Square Root of 119?
8.How do technology and digital tools in Canada support learning Algebra and Square Root of 119?
9.Does learning Algebra support future career opportunities for students in Canada?
Important Glossaries for Square Root of 119
- Perfect Square: Product obtained when the same number gets multiplied twice
- Approximate Value: Value closer to the exact number
- Prime Factorization: Breaking down the number into its prime factors.
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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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