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Square Root of 222

The square root of 222 is expressed as √222 in the radical form and as (222)^½ or (222)^0.5 in the exponent form. The square root of 222 rounded up to 9 decimal places is 14.899664426. It is the positive solution of the equation x² = 222.

Square Root of 222: 14.89966442575134
Square Root of 222 in exponential form: (222)^½ or (222)^0.5
Square Root of 222 in radical form: √222

Square Root of 222

1.	What is the Square Root of 222?
2.	How to find the Square Root of 222?
3.	Is the Square Root of 222 Irrational?
4.	FAQs

What is the Square Root of 222?

The square root of 222, (or root 222), is the number which when multiplied by itself gives the product as 222. Therefore, the square root of 222 = √222 = 14.89966442575134.

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How to Find Square Root of 222?

Square Root of 222 by Long Division Method

Value of √222 by Long Division Method

Explanation:

Forming pairs: 02 and 22
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 22, to the right of the remainder 1. The new dividend is now 122.
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 <= 122. After finding Z, together 2 and Z (4) form a new divisor 24 for the new dividend 122.
Divide 122 by 24 with the quotient as 4, giving the remainder = 122 - 24 × 4 = 122 - 96 = 26.
Now, let's find the decimal places after the quotient 14.
Bring down 00 to the right of this remainder 26. The new dividend is now 2600.
Add the last digit of quotient to divisor i.e. 4 + 24 = 28. To the right of 28, find a digit Z (which is 8) such that 28Z × Z <= 2600. Together they form a new divisor (288) for the new dividend (2600).
Divide 2600 by 288 with the quotient as 8, giving the remainder = 2600 - 288 × 8 = 2600 - 2304 = 296.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 222.

Therefore, the square root of 222 by long division method is 14.8 approx.

Is Square Root of 222 Irrational?

The actual value of √222 is undetermined. The value of √222 up to 25 decimal places is 14.89966442575133971933182. Hence, the square root of 222 is an irrational number.

☛ Also Check:

Square Root of 116 - √116 = 10.77033
Square Root of 325 - √325 = 18.02776
Square Root of 2 - √2 = 1.41421
Square Root of 37 - √37 = 6.08276
Square Root of 200 - √200 = 14.14214
Square Root of 27 - √27 = 5.19615
Square Root of 19 - √19 = 4.35890

Square Root of 222 Solved Examples

Example 1: Solve the equation x² − 222 = 0

Solution:

x² - 222 = 0 i.e. x² = 222
x = ±√222
Since the value of the square root of 222 is 14.900,
⇒ x = +√222 or -√222 = 14.900 or -14.900.
Example 2: If the surface area of a cube is 1332 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 = 1332 in²
⇒ a = ±√222 in
Since length can't be negative,
⇒ a = √222
We know that the square root of 222 is 14.900.
⇒ a = 14.900 in
Example 3: If the surface area of a sphere is 888π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 888π in²
⇒ r = ±√222 in
Since radius can't be negative,
⇒ r = √222
The square root of 222 is 14.900.
⇒ r = 14.900 in

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FAQs on the Square Root of 222

What is the Value of the Square Root of 222?

The square root of 222 is 14.89966.

Why is the Square Root of 222 an Irrational Number?

Upon prime factorizing 222 i.e. 2¹ × 3¹ × 37¹, 2 is in odd power. Therefore, the square root of 222 is irrational.

Is the number 222 a Perfect Square?

The prime factorization of 222 = 2¹ × 3¹ × 37¹. Here, the prime factor 2 is not in the pair. Therefore, 222 is not a perfect square.

If the Square Root of 222 is 14.900. Find the Value of the Square Root of 2.22.

Let us represent √2.22 in p/q form i.e. √(222/100) = 2.22/10 = 1.490. Hence, the value of √2.22 = 1.490

Evaluate 9 plus 15 square root 222

The given expression is 9 + 15 √222. We know that the square root of 222 is 14.900. Therefore, 9 + 15 √222 = 9 + 15 × 14.900 = 9 + 223.495 = 232.495

What is the Square of the Square Root of 222?

The square of the square root of 222 is the number 222 itself i.e. (√222)² = (222)^2/2 = 222.

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