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Square Root of 199

The square root of 199 is expressed as √199 in the radical form and as (199)^½ or (199)^0.5 in the exponent form. The square root of 199 rounded up to 9 decimal places is 14.106735980. It is the positive solution of the equation x² = 199.

Square Root of 199: 14.106735979665885
Square Root of 199 in exponential form: (199)^½ or (199)^0.5
Square Root of 199 in radical form: √199

Square Root of 199

1.	What is the Square Root of 199?
2.	How to find the Square Root of 199?
3.	Is the Square Root of 199 Irrational?
4.	FAQs

What is the Square Root of 199?

The square root of 199, (or root 199), is the number which when multiplied by itself gives the product as 199. Therefore, the square root of 199 = √199 = 14.106735979665885.

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How to Find Square Root of 199?

Square Root of 199 by Long Division Method

Value of √199 by Long Division Method

Explanation:

Forming pairs: 01 and 99
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 99, to the right of the remainder 0. The new dividend is now 99.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 4) such that 2Z × Z <= 99. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 99.
Divide 99 by 24 with the quotient as 4, giving the remainder = 99 - 24 × 4 = 99 - 96 = 3.
Now, let's find the decimal places after the quotient 14.
Bring down 00 to the right of this remainder 3. The new dividend is now 300.
Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 1) such that 28Z × Z <= 300. Together they form a new divisor (281) for the new dividend (300).
Divide 300 by 281 with the quotient as 1, giving the remainder = 300 - 281 × 1 = 300 - 281 = 19.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 199.

Therefore, the square root of 199 by long division method is 14.1 approx.

Is Square Root of 199 Irrational?

The actual value of √199 is undetermined. The value of √199 up to 25 decimal places is 14.10673597966588442523216. Hence, the square root of 199 is an irrational number.

☛ Also Check:

Square Root of 99 - √99 = 9.94987
Square Root of 288 - √288 = 16.97056
Square Root of 105 - √105 = 10.24695
Square Root of 52 - √52 = 7.21110
Square Root of 116 - √116 = 10.77033
Square Root of 76 - √76 = 8.71780
Square Root of 162 - √162 = 12.72792

Square Root of 199 Solved Examples

Example 1: Solve the equation x² − 199 = 0

Solution:

x² - 199 = 0 i.e. x² = 199
x = ±√199
Since the value of the square root of 199 is 14.107,
⇒ x = +√199 or -√199 = 14.107 or -14.107.
Example 2: If the surface area of a sphere is 796π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 796π in²
⇒ r = ±√199 in
Since radius can't be negative,
⇒ r = √199
The square root of 199 is 14.107.
⇒ r = 14.107 in
Example 3: If the area of a square is 199 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 199 in²
⇒ a = ±√199 in
Since length can't be negative,
⇒ a = √199 = 14.107 in

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FAQs on the Square Root of 199

What is the Value of the Square Root of 199?

The square root of 199 is 14.10673.

Why is the Square Root of 199 an Irrational Number?

The number 199 is prime. This implies that the number 199 is pairless and is not in the power of 2. Therefore, the square root of 199 is irrational.

What is the Value of 20 square root 199?

The square root of 199 is 14.107. Therefore, 20 √199 = 20 × 14.107 = 282.135.

What is the Square Root of -199?

The square root of -199 is an imaginary number. It can be written as √-199 = √-1 × √199 = i √199 = 14.106i
where i = √-1 and it is called the imaginary unit.

What is the Square Root of 199 in Simplest Radical Form?

The number 199 is a prime number. This implies that the number 199 is pairless and is not in the power of 2. Therefore, the radical form of square root of 199 cannot be simplified further.

If the Square Root of 199 is 14.107. Find the Value of the Square Root of 1.99.

Let us represent √1.99 in p/q form i.e. √(199/100) = 1.99/10 = 1.411. Hence, the value of √1.99 = 1.411

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