Square Root of 119
The square root of 119 is expressed as √119 in the radical form and as (119)^{½} or (119)^{0.5} in the exponent form. The square root of 119 rounded up to 8 decimal places is 10.90871211. It is the positive solution of the equation x^{2} = 119.
 Square Root of 119: 10.908712114635714
 Square Root of 119 in exponential form: (119)^{½} or (119)^{0.5}
 Square Root of 119 in radical form: √119
1.  What Is the Square Root of 119? 
2.  Is Square Root of 19 Rational or Irrational? 
3.  How to Find the Square Root of 119? 
4.  Tips and Tricks 
5.  FAQs on Square Root of 119 
6.  Challenging Questions 
What Is the Square Root of 119?
 The square root of 119 ⇒ √119 = √(a × a). Thus a = √119
 . √119 = √(10.908 × 10.908) or √(10.908 × 10.908) ⇒ √119 = ±10.908
 We know that on prime factorization, 119 = 7 × 17. Thus √119 cannot be expressed in the simplest radical form. The radical form of √119 is √119.
Is Square Root of 119 Rational or Irrational?
Irrational numbers are the real numbers that cannot be expressed as the ratio of two integers. √119 = 10.90871211463571 and hence the square root of 119 is an irrational number where the numbers after the decimal point go up to infinity.
How to Find the Square Root of 119?
The square root of 119 or any number can be calculated in many ways. Two of them are the approximation method and the long division method.
Square Root of 119 by Approximation Method
 Take two perfect square numbers, one of which is just smaller than 119 and another one just greater than 119. √100 < √119 < √121
 10 < √ 119 < 11
 Using the average method, divide 119 by 10 or 11.
 Let us divide by 11 ⇒ 119 ÷ 11 = 10.818
 Find the average of 10.818 and 11.
 (10.818 + 11) / 2 = 21.818 ÷ 2 = 10.909
 √119 ≈ 10.909
Square Root of 119 by the Long Division Method
The long division method helps us to find a more accurate value of square root of any number. The following are the steps to evaluate the square root of 119 by the long division method.
 Step 1: Write 119.000000. Take the number in pairs from the right. 1 stands alone. Now divide 1 by a number such that (number × number) gives ≤ 1.
 Obtain quotient = 1 and remainder = 0. Double the quotient. We get 2. Have 20 as our new divisor.
 Step 2: Find a number such that (20 + that number) × that number gives the product ≤ 16. We cannot find a number that divides 16. Bring down two zeros. 19 00 is our new dividend.
 10 is our quotient and on doubling, it becomes 20 and 200 is our new divisor. Find a number such that (200 + the number) × number gets 19 00 or less than that. We find 9 is such number. 209 × 9 = 18 81
 Step 3: Quotient is 10.9 and the remainder is 19. Bring down the next pair of zeros and 19 00 becomes the new dividend.
 Double the quotient. 109 × 2 = 218. Have 2180 in the place of the new divisor. Find a number such that (2180 + that number) × number ≤ 19 00.
 We cannot find a number that divides 19 00. Bring down two zeros. 19 00 00 is our new dividend.
 Quotient is 10.90 . Doubling it we get 2180.
 Repeat the steps until we approximate the square root to 3 decimal places. √119 = 10.908
Explore square roots using illustrations and interactive examples
Tips and Tricks
 The square root of 119 lies between the square root of 100 and 121. Therefore, 10 < √119 < 11. It is closer to the perfect square 121.
 19 is the least number to be subtracted and 2 is the least number to be added to make it a perfect square. (119  19 = 100) and (119 + 2 = 121)
Challenging Questions
 Find the square root of 119 up to 7 decimal places.
 Find the square root of √119.
Square Root of 119 Solved Examples

Example 1: Oneseventh of the square of a number is equal to 17. Kate is trying to find that number. Help her find the number approximated to the nearest tenth.
Solution: Oneseventh of a square of a number = 17
Le the number be x. Thus we have (1/7) x^{2} = 17
(1/7) x^{2} = 17 ⇒ x^{2} = 17 × 7
x^{2} = 119
x = √119
x = ±10.908
x ≈ 10.9

Example 2: Evaluate √1.19
Solution: √1.19 = √(119/100) = √119/√100
√119 = 10.908
√100 = 10
√119/√100 = 10.908 ÷ 10 = 1.0908
√1.19 = 1.0908

Example: Solve the equation x^{2} − 119 = 0
Solution:
x^{2}  119 = 0 i.e. x^{2} = 119
x = ±√119
Since the value of the square root of 119 is 10.909,
⇒ x = +√119 or √119 = 10.909 or 10.909.
FAQs on the Square Root of 119
What is the Value of the Square Root of 119?
The square root of 119 is 10.90871.
Why is the Square Root of 119 an Irrational Number?
Upon prime factorizing 119 i.e. 7^{1} × 17^{1}, 7 is in odd power. Therefore, the square root of 119 is irrational.
If the Square Root of 119 is 10.909. Find the Value of the Square Root of 1.19.
Let us represent √1.19 in p/q form i.e. √(119/100) = 1.19/10 = 1.091. Hence, the value of √1.19 = 1.091
What is the Value of 15 square root 119?
The square root of 119 is 10.909. Therefore, 15 √119 = 15 × 10.909 = 163.631.
What is the Square Root of 119?
The square root of 119 is an imaginary number. It can be written as √119 = √1 × √119 = i √119 = 10.908i
where i = √1 and it is called the imaginary unit.
What is the Square Root of 119 in Simplest Radical Form?
We need to express 119 as the product of its prime factors i.e. 119 = 7 × 17. Therefore, as visible, the radical form of the square root of 119 cannot be simplified further. Therefore, the simplest radical form of the square root of 119 can be written as √119
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