Square Root of 129
The square root of 129 is expressed as √129 in the radical form and as (129)^{½} or (129)^{0.5} in the exponent form. The square root of 129 rounded up to 9 decimal places is 11.357816692. It is the positive solution of the equation x^{2} = 129.
 Square Root of 129: 11.357816691600547
 Square Root of 129 in exponential form: (129)^{½} or (129)^{0.5}
 Square Root of 129 in radical form: √129
1.  What is the Square Root of 129? 
2.  How to find the Square Root of 129? 
3.  Is the Square Root of 129 Irrational? 
4.  FAQs 
What is the Square Root of 129?
The square root of 129, (or root 129), is the number which when multiplied by itself gives the product as 129. Therefore, the square root of 129 = √129 = 11.357816691600547.
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How to Find Square Root of 129?
Value of √129 by Long Division Method
Explanation:
 Forming pairs: 01 and 29
 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 29, to the right of the remainder 0. The new dividend is now 29.
 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 1) such that 2Z × Z <= 29. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 29.
 Divide 29 by 21 with the quotient as 1, giving the remainder = 29  21 × 1 = 29  21 = 8.
 Now, let's find the decimal places after the quotient 11.
 Bring down 00 to the right of this remainder 8. The new dividend is now 800.
 Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 3) such that 22Z × Z <= 800. Together they form a new divisor (223) for the new dividend (800).
 Divide 800 by 223 with the quotient as 3, giving the remainder = 800  223 × 3 = 800  669 = 131.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 129.
Therefore, the square root of 129 by long division method is 11.3 approximately.
Is Square Root of 129 Irrational?
The actual value of √129 is undetermined. The value of √129 up to 25 decimal places is 11.35781669160054722178468. Hence, the square root of 129 is an irrational number.
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 Square Root of 13  √13 = 3.60555
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Square Root of 129 Solved Examples

Example 1: Solve the equation x^{2} − 129 = 0
Solution:
x^{2}  129 = 0 i.e. x^{2} = 129
x = ±√129
Since the value of the square root of 129 is 11.358,
⇒ x = +√129 or √129 = 11.358 or 11.358. 
Example 2: If the surface area of a sphere is 516π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 516π in^{2}
⇒ r = ±√129 in
Since radius can't be negative,
⇒ r = √129
The square root of 129 is 11.358.
⇒ r = 11.358 in 
Example 3: If the surface area of a cube is 774 in^{2}. 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 = 6a^{2} = 774 in^{2}
⇒ a = ±√129 in
Since length can't be negative,
⇒ a = √129
We know that the square root of 129 is 11.358.
⇒ a = 11.358 in
FAQs on the Square Root of 129
What is the Value of the Square Root of 129?
The square root of 129 is 11.35781.
Why is the Square Root of 129 an Irrational Number?
Upon prime factorizing 129 i.e. 3^{1} × 43^{1}, 3 is in odd power. Therefore, the square root of 129 is irrational.
Evaluate 11 plus 6 square root 129
The given expression is 11 + 6 √129. We know that the square root of 129 is 11.358. Therefore, 11 + 6 √129 = 11 + 6 × 11.358 = 11 + 68.147 = 79.147
Is the number 129 a Perfect Square?
The prime factorization of 129 = 3^{1} × 43^{1}. Here, the prime factor 3 is not in the pair. Therefore, 129 is not a perfect square.
What is the Value of 9 square root 129?
The square root of 129 is 11.358. Therefore, 9 √129 = 9 × 11.358 = 102.220.
What is the Square Root of 129?
The square root of 129 is an imaginary number. It can be written as √129 = √1 × √129 = i √129 = 11.357i
where i = √1 and it is called the imaginary unit.