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Square Root of 191

The square root of 191 is expressed as √191 in the radical form and as (191)^½ or (191)^0.5 in the exponent form. The square root of 191 rounded up to 9 decimal places is 13.820274961. It is the positive solution of the equation x² = 191.

Square Root of 191: 13.820274961085254
Square Root of 191 in exponential form: (191)^½ or (191)^0.5
Square Root of 191 in radical form: √191

Square Root of 191

1.	What is the Square Root of 191?
2.	How to find the Square Root of 191?
3.	Is the Square Root of 191 Irrational?
4.	FAQs

What is the Square Root of 191?

The square root of 191, (or root 191), is the number which when multiplied by itself gives the product as 191. Therefore, the square root of 191 = √191 = 13.820274961085254.

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How to Find Square Root of 191?

Square Root of 191 by Long Division Method

Value of √191 by Long Division Method

Explanation:

Forming pairs: 01 and 91
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 91, to the right of the remainder 0. The new dividend is now 91.
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 3) such that 2Z × Z <= 91. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 91.
Divide 91 by 23 with the quotient as 3, giving the remainder = 91 - 23 × 3 = 91 - 69 = 22.
Now, let's find the decimal places after the quotient 13.
Bring down 00 to the right of this remainder 22. The new dividend is now 2200.
Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 8) such that 26Z × Z <= 2200. Together they form a new divisor (268) for the new dividend (2200).
Divide 2200 by 268 with the quotient as 8, giving the remainder = 2200 - 268 × 8 = 2200 - 2144 = 56.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 191.

Therefore, the square root of 191 by long division method is 13.8 approximately.

Is Square Root of 191 Irrational?

The actual value of √191 is undetermined. The value of √191 up to 25 decimal places is 13.82027496108525331390448. Hence, the square root of 191 is an irrational number.

☛ Also Check:

Square Root of 116 - √116 = 10.77033
Square Root of 841 - √841 = 29
Square Root of 28 - √28 = 5.29150
Square Root of 76 - √76 = 8.71780
Square Root of 8 - √8 = 2.82843
Square Root of 29 - √29 = 5.38516
Square Root of 48 - √48 = 6.92820

Square Root of 191 Solved Examples

Example 1: Solve the equation x² − 191 = 0

Solution:

x² - 191 = 0 i.e. x² = 191
x = ±√191
Since the value of the square root of 191 is 13.820,
⇒ x = +√191 or -√191 = 13.820 or -13.820.
Example 2: If the surface area of a cube is 1146 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 1146 in²
⇒ a = ±√191 in
Since length can't be negative,
⇒ a = √191
We know that the square root of 191 is 13.820.
⇒ a = 13.820 in
Example 3: If the surface area of a sphere is 764π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 764π in²
⇒ r = ±√191 in
Since radius can't be negative,
⇒ r = √191
The square root of 191 is 13.820.
⇒ r = 13.820 in

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FAQs on the Square Root of 191

What is the Value of the Square Root of 191?

The square root of 191 is 13.82027.

Why is the Square Root of 191 an Irrational Number?

The number 191 is prime. This implies that the number 191 is pairless and is not in the power of 2. Therefore, the square root of 191 is irrational.

What is the Square of the Square Root of 191?

The square of the square root of 191 is the number 191 itself i.e. (√191)² = (191)^2/2 = 191.

What is the Square Root of -191?

The square root of -191 is an imaginary number. It can be written as √-191 = √-1 × √191 = i √191 = 13.82i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 191 is 13.820. Find the Value of the Square Root of 1.91.

Let us represent √1.91 in p/q form i.e. √(191/100) = 1.91/10 = 1.382. Hence, the value of √1.91 = 1.382

Is the number 191 a Perfect Square?

The number 191 is prime. This implies that the square root of 191 cannot be expressed as a product of two equal integers. Therefore, the number 191 is not a perfect square.

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