Square Root of 137
The square root of 137 is expressed as √137 in the radical form and as (137)^{½} or (137)^{0.5} in the exponent form. The square root of 137 rounded up to 7 decimal places is 11.7046999. It is the positive solution of the equation x^{2} = 137.
 Square Root of 137: 11.704699910719626
 Square Root of 137 in exponential form: (137)^{½} or (137)^{0.5}
 Square Root of 137 in radical form: √137
1.  What is the Square Root of 137? 
2.  How to find the Square Root of 137? 
3.  Is the Square Root of 137 Irrational? 
4.  FAQs 
What is the Square Root of 137?
The square root of 137, (or root 137), is the number which when multiplied by itself gives the product as 137. Therefore, the square root of 137 = √137 = 11.704699910719626.
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How to Find Square Root of 137?
Value of √137 by Long Division Method
Explanation:
 Forming pairs: 01 and 37
 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 37, to the right of the remainder 0. The new dividend is now 37.
 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 <= 37. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 37.
 Divide 37 by 21 with the quotient as 1, giving the remainder = 37  21 × 1 = 37  21 = 16.
 Now, let's find the decimal places after the quotient 11.
 Bring down 00 to the right of this remainder 16. The new dividend is now 1600.
 Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 7) such that 22Z × Z <= 1600. Together they form a new divisor (227) for the new dividend (1600).
 Divide 1600 by 227 with the quotient as 7, giving the remainder = 1600  227 × 7 = 1600  1589 = 11.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 137.
Therefore, the square root of 137 by long division method is 11.7 approx.
Is Square Root of 137 Irrational?
The actual value of √137 is undetermined. The value of √137 up to 25 decimal places is 11.70469991071962510910210. Hence, the square root of 137 is an irrational number.
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 Square Root of 17  √17 = 4.12311
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 Square Root of 48  √48 = 6.92820
 Square Root of 16  √16 = 4
 Square Root of 14  √14 = 3.74166
 Square Root of 200  √200 = 14.14214
Square Root of 137 Solved Examples

Example 1: Solve the equation x^{2} − 137 = 0
Solution:
x^{2}  137 = 0 i.e. x^{2} = 137
x = ±√137
Since the value of the square root of 137 is 11.705,
⇒ x = +√137 or √137 = 11.705 or 11.705. 
Example 2: If the surface area of a sphere is 548π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 548π in^{2}
⇒ r = ±√137 in
Since radius can't be negative,
⇒ r = √137
The square root of 137 is 11.705.
⇒ r = 11.705 in 
Example 3: If the surface area of a cube is 822 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} = 822 in^{2}
⇒ a = ±√137 in
Since length can't be negative,
⇒ a = √137
We know that the square root of 137 is 11.705.
⇒ a = 11.705 in
FAQs on the Square Root of 137
What is the Value of the Square Root of 137?
The square root of 137 is 11.70469.
Why is the Square Root of 137 an Irrational Number?
The number 137 is prime. This implies that the number 137 is pairless and is not in the power of 2. Therefore, the square root of 137 is irrational.
What is the Square Root of 137 in Simplest Radical Form?
The number 137 is a prime number. This implies that the number 137 is pairless and is not in the power of 2. Therefore, the radical form of square root of 137 cannot be simplified further.
If the Square Root of 137 is 11.705. Find the Value of the Square Root of 1.37.
Let us represent √1.37 in p/q form i.e. √(137/100) = 1.37/10 = 1.170. Hence, the value of √1.37 = 1.170
Is the number 137 a Perfect Square?
The number 137 is prime. This implies that the square root of 137 cannot be expressed as a product of two equal integers. Therefore, the number 137 is not a perfect square.
Evaluate 9 plus 8 square root 137
The given expression is 9 + 8 √137. We know that the square root of 137 is 11.705. Therefore, 9 + 8 √137 = 9 + 8 × 11.705 = 9 + 93.638 = 102.638