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 x^{2} = 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
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?
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.
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Square Root of 229 Solved Examples

Example 1: Solve the equation x^{2} − 229 = 0
Solution:
x^{2}  229 = 0 i.e. x^{2} = 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 in^{2}. 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 = a^{2} = 229 in^{2}
⇒ a = ±√229 in
Since length can't be negative,
⇒ a = √229 = 15.133 in 
Example 3: If the area of a circle is 229π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 229π in^{2}
⇒ r = ±√229 in
Since radius can't be negative,
⇒ r = √229
The square root of 229 is 15.133.
⇒ r = 15.133 in
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