Square Root of 228

The square root of 228 is expressed as √228 in the radical form and as (228)^½ or (228)^0.5 in the exponent form. The square root of 228 rounded up to 9 decimal places is 15.099668871. It is the positive solution of the equation x² = 228. We can express the square root of 228 in its lowest radical form as 2 √57.

Square Root of 228: 15.0996688705415
Square Root of 228 in exponential form: (228)^½ or (228)^0.5
Square Root of 228 in radical form: √228 or 2 √57

Square Root of 228

1.	What is the Square Root of 228?
2.	How to find the Square Root of 228?
3.	Is the Square Root of 228 Irrational?
4.	FAQs

What is the Square Root of 228?

The square root of 228, (or root 228), is the number which when multiplied by itself gives the product as 228. Therefore, the square root of 228 = √228 = 2 √57 = 15.0996688705415.

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How to Find Square Root of 228?

Square Root of 228 by Long Division Method

Value of √228 by Long Division Method

Explanation:

Forming pairs: 02 and 28
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 28, to the right of the remainder 1. The new dividend is now 128.
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 5) such that 2Z × Z <= 128. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 128.
Divide 128 by 25 with the quotient as 5, giving the remainder = 128 - 25 × 5 = 128 - 125 = 3.
Now, let's find the decimal places after the quotient 15.
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. 5 + 25 = 30. To the right of 30, find a digit Z (which is 0) such that 30Z × Z <= 300. Together they form a new divisor (300) for the new dividend (300).
Divide 300 by 300 with the quotient as 0, giving the remainder = 300 - 300 × 0 = 300 - 0 = 300.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 228.

Therefore, the square root of 228 by long division method is 15.0 approximately.

Is Square Root of 228 Irrational?

The actual value of √228 is undetermined. The value of √228 up to 25 decimal places is 15.09966887054149939447337. Hence, the square root of 228 is an irrational number.

☛ Also Check:

Square Root of 512 - √512 = 22.62742
Square Root of 90 - √90 = 9.48683
Square Root of 225 - √225 = 15
Square Root of 2 - √2 = 1.41421
Square Root of 44 - √44 = 6.63325
Square Root of 39 - √39 = 6.24500
Square Root of 15 - √15 = 3.87298

Square Root of 228 Solved Examples

Example 1: Solve the equation x² − 228 = 0

Solution:

x² - 228 = 0 i.e. x² = 228
x = ±√228
Since the value of the square root of 228 is 15.100,
⇒ x = +√228 or -√228 = 15.100 or -15.100.
Example 2: If the surface area of a cube is 1368 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 = 1368 in²
⇒ a = ±√228 in
Since length can't be negative,
⇒ a = √228
We know that the square root of 228 is 15.100.
⇒ a = 15.100 in
Example 3: If the area of a circle is 228π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 228π in²
⇒ r = ±√228 in
Since radius can't be negative,
⇒ r = √228
The square root of 228 is 15.100.
⇒ r = 15.100 in

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FAQs on the Square Root of 228

What is the Value of the Square Root of 228?

The square root of 228 is 15.09966.

Why is the Square Root of 228 an Irrational Number?

Upon prime factorizing 228 i.e. 2² × 3¹ × 19¹, 3 is in odd power. Therefore, the square root of 228 is irrational.

What is the Square of the Square Root of 228?

The square of the square root of 228 is the number 228 itself i.e. (√228)² = (228)^2/2 = 228.

What is the Value of 14 square root 228?

The square root of 228 is 15.100. Therefore, 14 √228 = 14 × 15.100 = 211.395.

Evaluate 10 plus 9 square root 228

The given expression is 10 + 9 √228. We know that the square root of 228 is 15.100. Therefore, 10 + 9 √228 = 10 + 9 × 15.100 = 10 + 135.897 = 145.897

If the Square Root of 228 is 15.100. Find the Value of the Square Root of 2.28.

Let us represent √2.28 in p/q form i.e. √(228/100) = 2.28/10 = 1.510. Hence, the value of √2.28 = 1.510

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