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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 x² = 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

Square Root of 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?

Square Root of 137 by Long Division Method

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.

☛ Also Check:

Square Root of 17 - √17 = 4.12311
Square Root of 97 - √97 = 9.84886
Square Root of 75 - √75 = 8.66025
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 x² − 137 = 0

Solution:

x² - 137 = 0 i.e. x² = 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 in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 548π in²
⇒ 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 in². 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 = 6a² = 822 in²
⇒ 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

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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

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