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Square Root of 229

The square root of 229 is expressed as √229 in the radical form and as (229)^½ or (229)^0.5 in the exponent form. The square root of 229 rounded up to 6 decimal places is 15.132746. It is the positive solution of the equation x² = 229.

Square Root of 229: 15.132745950421556
Square Root of 229 in exponential form: (229)^½ or (229)^0.5
Square Root of 229 in radical form: √229

Square Root of 229

1.	What is the Square Root of 229?
2.	How to find the Square Root of 229?
3.	Is the Square Root of 229 Irrational?
4.	FAQs

What is the Square Root of 229?

The square root of 229, (or root 229), is the number which when multiplied by itself gives the product as 229. Therefore, the square root of 229 = √229 = 15.132745950421556.

☛ Check: Square Root Calculator

How to Find Square Root of 229?

Square Root of 229 by Long Division Method

Value of √229 by Long Division Method

Explanation:

Forming pairs: 02 and 29
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 29, to the right of the remainder 1. The new dividend is now 129.
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 <= 129. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 129.
Divide 129 by 25 with the quotient as 5, giving the remainder = 129 - 25 × 5 = 129 - 125 = 4.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 4. The new dividend is now 400.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 1) such that 30Z × Z <= 400. Together they form a new divisor (301) for the new dividend (400).
Divide 400 by 301 with the quotient as 1, giving the remainder = 400 - 301 × 1 = 400 - 301 = 99.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 229.

Therefore, the square root of 229 by long division method is 15.1 approx.

Is Square Root of 229 Irrational?

The actual value of √229 is undetermined. The value of √229 up to 25 decimal places is 15.13274595042155592719186. Hence, the square root of 229 is an irrational number.

☛ Also Check:

Square Root of 74 - √74 = 8.60233
Square Root of 39 - √39 = 6.24500
Square Root of 200 - √200 = 14.14214
Square Root of 13 - √13 = 3.60555
Square Root of 68 - √68 = 8.24621
Square Root of 36 - √36 = 6
Square Root of 89 - √89 = 9.43398

Square Root of 229 Solved Examples

Example 1: Solve the equation x² − 229 = 0

Solution:

x² - 229 = 0 i.e. x² = 229
x = ±√229
Since the value of the square root of 229 is 15.133,
⇒ x = +√229 or -√229 = 15.133 or -15.133.
Example 2: If the area of a square is 229 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 = 229 in²
⇒ a = ±√229 in
Since length can't be negative,
⇒ a = √229 = 15.133 in
Example 3: If the area of a circle is 229π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 229π in²
⇒ r = ±√229 in
Since radius can't be negative,
⇒ r = √229
The square root of 229 is 15.133.
⇒ r = 15.133 in

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FAQs on the Square Root of 229

What is the Value of the Square Root of 229?

The square root of 229 is 15.13274.

Why is the Square Root of 229 an Irrational Number?

The number 229 is prime. This implies that the number 229 is pairless and is not in the power of 2. Therefore, the square root of 229 is irrational.

What is the Square of the Square Root of 229?

The square of the square root of 229 is the number 229 itself i.e. (√229)² = (229)^2/2 = 229.

What is the Square Root of -229?

The square root of -229 is an imaginary number. It can be written as √-229 = √-1 × √229 = i √229 = 15.132i
where i = √-1 and it is called the imaginary unit.

What is the Value of 8 square root 229?

The square root of 229 is 15.133. Therefore, 8 √229 = 8 × 15.133 = 121.062.

Evaluate 20 plus 20 square root 229

The given expression is 20 + 20 √229. We know that the square root of 229 is 15.133. Therefore, 20 + 20 √229 = 20 + 20 × 15.133 = 20 + 302.655 = 322.655

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