Square Root of 127
The square root of 127 is expressed as √127 in the radical form and as (127)^{½} or (127)^{0.5} in the exponent form. The square root of 127 rounded up to 10 decimal places is 11.2694276696. It is the positive solution of the equation x^{2} = 127.
 Square Root of 127: 11.269427669584644
 Square Root of 127 in exponential form: (127)^{½} or (127)^{0.5}
 Square Root of 127 in radical form: √127
1.  What is the Square Root of 127? 
2.  How to find the Square Root of 127? 
3.  Is the Square Root of 127 Irrational? 
4.  FAQs 
What is the Square Root of 127?
The square root of 127, (or root 127), is the number which when multiplied by itself gives the product as 127. Therefore, the square root of 127 = √127 = 11.269427669584644.
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How to Find Square Root of 127?
Value of √127 by Long Division Method
Explanation:
 Forming pairs: 01 and 27
 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 27, to the right of the remainder 0. The new dividend is now 27.
 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 <= 27. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 27.
 Divide 27 by 21 with the quotient as 1, giving the remainder = 27  21 × 1 = 27  21 = 6.
 Now, let's find the decimal places after the quotient 11.
 Bring down 00 to the right of this remainder 6. The new dividend is now 600.
 Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 2) such that 22Z × Z <= 600. Together they form a new divisor (222) for the new dividend (600).
 Divide 600 by 222 with the quotient as 2, giving the remainder = 600  222 × 2 = 600  444 = 156.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 127.
Therefore, the square root of 127 by long division method is 11.2 approx.
Is Square Root of 127 Irrational?
The actual value of √127 is undetermined. The value of √127 up to 25 decimal places is 11.26942766958464488285000. Hence, the square root of 127 is an irrational number.
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 Square Root of 76  √76 = 8.71780
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 Square Root of 80  √80 = 8.94427
 Square Root of 106  √106 = 10.29563
 Square Root of 149  √149 = 12.20656
 Square Root of 113  √113 = 10.63015
 Square Root of 17  √17 = 4.12311
Square Root of 127 Solved Examples

Example 1: Solve the equation x^{2} − 127 = 0
Solution:
x^{2}  127 = 0 i.e. x^{2} = 127
x = ±√127
Since the value of the square root of 127 is 11.269,
⇒ x = +√127 or √127 = 11.269 or 11.269. 
Example 2: If the surface area of a sphere is 508π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 508π in^{2}
⇒ r = ±√127 in
Since radius can't be negative,
⇒ r = √127
The square root of 127 is 11.269.
⇒ r = 11.269 in 
Example 3: If the area of a square is 127 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} = 127 in^{2}
⇒ a = ±√127 in
Since length can't be negative,
⇒ a = √127 = 11.269 in
FAQs on the Square Root of 127
What is the Value of the Square Root of 127?
The square root of 127 is 11.26942.
Why is the Square Root of 127 an Irrational Number?
The number 127 is prime. This implies that the number 127 is pairless and is not in the power of 2. Therefore, the square root of 127 is irrational.
What is the Square Root of 127 in Simplest Radical Form?
The number 127 is a prime number. This implies that the number 127 is pairless and is not in the power of 2. Therefore, the radical form of square root of 127 cannot be simplified further.
Evaluate 13 plus 19 square root 127
The given expression is 13 + 19 √127. We know that the square root of 127 is 11.269. Therefore, 13 + 19 √127 = 13 + 19 × 11.269 = 13 + 214.119 = 227.119
What is the Value of 2 square root 127?
The square root of 127 is 11.269. Therefore, 2 √127 = 2 × 11.269 = 22.539.
What is the Square of the Square Root of 127?
The square of the square root of 127 is the number 127 itself i.e. (√127)^{2} = (127)^{2/2} = 127.