Square Root of 261
The square root of 261 is expressed as √261 in the radical form and as (261)^{½} or (261)^{0.5} in the exponent form. The square root of 261 rounded up to 9 decimal places is 16.155494421. It is the positive solution of the equation x^{2} = 261. We can express the square root of 261 in its lowest radical form as 3 √29.
 Square Root of 261: 16.15549442140351
 Square Root of 261 in exponential form: (261)^{½} or (261)^{0.5}
 Square Root of 261 in radical form: √261 or 3 √29
1.  What is the Square Root of 261? 
2.  How to find the Square Root of 261? 
3.  Is the Square Root of 261 Irrational? 
4.  FAQs 
What is the Square Root of 261?
The square root of 261, (or root 261), is the number which when multiplied by itself gives the product as 261. Therefore, the square root of 261 = √261 = 3 √29 = 16.15549442140351.
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How to Find Square Root of 261?
Value of √261 by Long Division Method
Explanation:
 Forming pairs: 02 and 61
 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 61, to the right of the remainder 1. The new dividend is now 161.
 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 6) such that 2Z × Z <= 161. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 161.
 Divide 161 by 26 with the quotient as 6, giving the remainder = 161  26 × 6 = 161  156 = 5.
 Now, let's find the decimal places after the quotient 16.
 Bring down 00 to the right of this remainder 5. The new dividend is now 500.
 Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 1) such that 32Z × Z <= 500. Together they form a new divisor (321) for the new dividend (500).
 Divide 500 by 321 with the quotient as 1, giving the remainder = 500  321 × 1 = 500  321 = 179.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 261.
Therefore, the square root of 261 by long division method is 16.1 approximately.
Is Square Root of 261 Irrational?
The actual value of √261 is undetermined. The value of √261 up to 25 decimal places is 16.15549442140351209375213. Hence, the square root of 261 is an irrational number.
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 Square Root of 33  √33 = 5.74456
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 Square Root of 73  √73 = 8.54400
 Square Root of 75  √75 = 8.66025
 Square Root of 13  √13 = 3.60555
Square Root of 261 Solved Examples

Example 1: Solve the equation x^{2} − 261 = 0
Solution:
x^{2}  261 = 0 i.e. x^{2} = 261
x = ±√261
Since the value of the square root of 261 is 16.155,
⇒ x = +√261 or √261 = 16.155 or 16.155. 
Example 2: If the surface area of a sphere is 1044π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 1044π in^{2}
⇒ r = ±√261 in
Since radius can't be negative,
⇒ r = √261
The square root of 261 is 16.155.
⇒ r = 16.155 in 
Example 3: If the surface area of a cube is 1566 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} = 1566 in^{2}
⇒ a = ±√261 in
Since length can't be negative,
⇒ a = √261
We know that the square root of 261 is 16.155.
⇒ a = 16.155 in
FAQs on the Square Root of 261
What is the Value of the Square Root of 261?
The square root of 261 is 16.15549.
Why is the Square Root of 261 an Irrational Number?
Upon prime factorizing 261 i.e. 3^{2} × 29^{1}, 29 is in odd power. Therefore, the square root of 261 is irrational.
What is the Square Root of 261 in Simplest Radical Form?
We need to express 261 as the product of its prime factors i.e. 261 = 3 × 3 × 29. Therefore, √261 = √3 × 3 × 29 = 3 √29. Thus, the square root of 261 in the lowest radical form is 3 √29.
If the Square Root of 261 is 16.155. Find the Value of the Square Root of 2.61.
Let us represent √2.61 in p/q form i.e. √(261/100) = 2.61/10 = 1.616. Hence, the value of √2.61 = 1.616
Is the number 261 a Perfect Square?
The prime factorization of 261 = 3^{2} × 29^{1}. Here, the prime factor 29 is not in the pair. Therefore, 261 is not a perfect square.
What is the Square of the Square Root of 261?
The square of the square root of 261 is the number 261 itself i.e. (√261)^{2} = (261)^{2/2} = 261.