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Square Root of 188

The square root of 188 is expressed as √188 in the radical form and as (188)^½ or (188)^0.5 in the exponent form. The square root of 188 rounded up to 10 decimal places is 13.7113092008. It is the positive solution of the equation x² = 188. We can express the square root of 188 in its lowest radical form as 2 √47.

Square Root of 188: 13.711309200802088
Square Root of 188 in exponential form: (188)^½ or (188)^0.5
Square Root of 188 in radical form: √188 or 2 √47

Square Root of 188

1.	What is the Square Root of 188?
2.	How to find the Square Root of 188?
3.	Is the Square Root of 188 Irrational?
4.	FAQs

What is the Square Root of 188?

The square root of 188, (or root 188), is the number which when multiplied by itself gives the product as 188. Therefore, the square root of 188 = √188 = 2 √47 = 13.711309200802088.

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How to Find Square Root of 188?

Square Root of 188 by Long Division Method

Value of √188 by Long Division Method

Explanation:

Forming pairs: 01 and 88
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 88, to the right of the remainder 0. The new dividend is now 88.
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 <= 88. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 88.
Divide 88 by 23 with the quotient as 3, giving the remainder = 88 - 23 × 3 = 88 - 69 = 19.
Now, let's find the decimal places after the quotient 13.
Bring down 00 to the right of this remainder 19. The new dividend is now 1900.
Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 7) such that 26Z × Z <= 1900. Together they form a new divisor (267) for the new dividend (1900).
Divide 1900 by 267 with the quotient as 7, giving the remainder = 1900 - 267 × 7 = 1900 - 1869 = 31.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 188.

Therefore, the square root of 188 by long division method is 13.7 approx.

Is Square Root of 188 Irrational?

The actual value of √188 is undetermined. The value of √188 up to 25 decimal places is 13.71130920080208824987174. Hence, the square root of 188 is an irrational number.

☛ Also Check:

Square Root of 200 - √200 = 14.14214
Square Root of 21 - √21 = 4.58258
Square Root of 90 - √90 = 9.48683
Square Root of 50 - √50 = 7.07107
Square Root of 400 - √400 = 20
Square Root of 75 - √75 = 8.66025
Square Root of 35 - √35 = 5.91608

Square Root of 188 Solved Examples

Example 1: Solve the equation x² − 188 = 0

Solution:

x² - 188 = 0 i.e. x² = 188
x = ±√188
Since the value of the square root of 188 is 13.711,
⇒ x = +√188 or -√188 = 13.711 or -13.711.
Example 2: If the surface area of a sphere is 752π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 752π in²
⇒ r = ±√188 in
Since radius can't be negative,
⇒ r = √188
The square root of 188 is 13.711.
⇒ r = 13.711 in
Example 3: If the area of a square is 188 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 = 188 in²
⇒ a = ±√188 in
Since length can't be negative,
⇒ a = √188 = 13.711 in

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FAQs on the Square Root of 188

What is the Value of the Square Root of 188?

The square root of 188 is 13.7113.

Why is the Square Root of 188 an Irrational Number?

Upon prime factorizing 188 i.e. 2² × 47¹, 47 is in odd power. Therefore, the square root of 188 is irrational.

Evaluate 9 plus 4 square root 188

The given expression is 9 + 4 √188. We know that the square root of 188 is 13.711. Therefore, 9 + 4 √188 = 9 + 4 × 13.711 = 9 + 54.845 = 63.845

Is the number 188 a Perfect Square?

The prime factorization of 188 = 2² × 47¹. Here, the prime factor 47 is not in the pair. Therefore, 188 is not a perfect square.

What is the Value of 1 square root 188?

The square root of 188 is 13.711. Therefore, 1 √188 = 1 × 13.711 = 13.711.

What is the Square Root of -188?

The square root of -188 is an imaginary number. It can be written as √-188 = √-1 × √188 = i √188 = 13.711i
where i = √-1 and it is called the imaginary unit.

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