The square root of 119 is expressed as √119 in the radical kind and as (119)½ or (119)0.5 in the exponent form. The square source of 119 rounded approximately 8 decimal places is 10.90871211. It is the optimistic solution of the equation x2 = 119.

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. √119 = √(10.908 × 10.908) or √(-10.908 × -10.908) ⇒ √119 = ±10.908We recognize that on prime factorization, 119 = 7 × 17. Thus √119 can not be expressed in the simplest radical form. The radical type of √119 is √119.

The square root of 119 or any kind of number deserve to be calculation in plenty of ways. Two of them space the approximation method and the long department method.

Square root of 119 through Approximation Method

Take two perfect square numbers, among which is just smaller than 119 and also another one just better than 119. √100 10 using the average method, division 119 by 10 or 11.Let us divide through 11 ⇒ 119 ÷ 11 = 10.818Find the typical of 10.818 and 11.(10.818 + 11) / 2 = 21.818 ÷ 2 = 10.909√119 ≈ 10.909

Square root of 119 through the Long department Method

The long department method helps us to discover a an ext accurate value of square root of any kind of number. The following are the steps to evaluate the square root of 119 by the long division method.

Step 1: create 119.000000. Take it the number in bag from the right. 1 was standing alone. Now divide 1 by a number such the (number × number) offers ≤ 1.Obtain quotient = 1 and remainder = 0. Double the quotient. We obtain 2. Have actually 20 as our brand-new divisor. Step 2: Find a number such the (20 + that number) × the number offers the product ≤ 16. We cannot uncover a number that divides 16. Carry down two zeros. 19 00 is our new dividend.10 is ours quotient and on doubling, it becomes 20 and 200 is our new divisor. Find a number such the (200 + the number) × number gets 19 00 or much less than that. We find 9 is together number. 209 × 9 = 18 81Step 3: Quotient is 10.9 and also the remainder is 19. Bring down the following pair of zeros and 19 00 i do not care the brand-new dividend. Double the quotient. 109 × 2 = 218. Have actually 2180  in the place of the brand-new divisor. Discover a number such the (2180 + the number) × number ≤ 19 00. We cannot find a number the divides 19 00. Bring down 2 zeros. 19 00 00 is our new dividend.Quotient is 10.90 . Doubling it we gain 2180.Repeat the steps until us approximate the square root to 3 decimal places. √119 = 10.908

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The square source of 119 lies in between the square source of 100 and also 121. Therefore, 10 19 is the the very least number to be subtracted and 2 is the the very least number to be added to make it a perfect square. (119 - 19 = 100) and (119 + 2 = 121)

Challenging Questions


Find the square source of 119 as much as 7 decimal places.Find the square source of 119.

Square source of 119 addressed Examples

 


Example 1: One-seventh that the square the a number is equal to 17. Kate is make the efforts to find that number. Aid her uncover the number approximated to the nearest tenth.

Solution: One-seventh of a square of a number = 17

Le the number be x. Therefore we have (1/7) x2 = 17 

(1/7) x2 = 17 ⇒ x2 = 17 × 7

x2 = 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: deal with the equation x2 − 119 = 0

Solution:

x2 - 119 = 0 i.e. X2 = 119x = ±√119Since the worth of the square source of 119 is 10.909,⇒ x = +√119 or -√119 = 10.909 or -10.909.


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FAQs top top the Square root of 119

What is the value of the Square source 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. 71 × 171, 7 is in odd power. Therefore, the square root of 119 is irrational.

If the Square root of 119 is 10.909. Discover the value of the Square root of 1.19.

Let us stand for √1.19 in p/q type i.e. √(119/100) = 1.19/10 = 1.091. Hence, the value of √1.19 = 1.091

What is the value of 15 square source 119?

The square root of 119 is 10.909. Therefore, 15 √119 = 15 × 10.909 = 163.631.

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What is the Square root of -119?

The square root of -119 is an imaginary number. It deserve to be composed as √-119 = √-1 × √119 = ns √119 = 10.908iwhere ns = √-1 and also it is referred to as the imaginary unit.

What is the Square source of 119 in easiest Radical Form?

We have to express 119 as the product the its prime factors i.e. 119 = 7 × 17. Therefore, as visible, the radical kind of the square root of 119 cannot be streamlined further. Therefore, the simplest radical type of the square root of 119 deserve to be composed as √119