The square root of 137 is expressed as √137 in the radical develop and also as (137)½ or (137)0.5 in the exponent create. The square root of 137 rounded as much as 7 decimal places is 11.7046999. It is the positive solution of the equation x2 = 137.

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Square Root of 137: 11.704699910719626Square Root of 137 in exponential form: (137)½ or (137)0.5Square Root of 137 in radical form: √137

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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

The square root of 137, (or root 137), is the number which once multiplied by itself provides the product as 137. Because of this, the square root of 137 = √137 = 11.704699910719626.

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Value of √137 by Long Division Method

Explanation:

Forming pairs: 01 and 37Find a number Y (1) such that whose square is Bring dvery own the following 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 best of 2, find a digit Z (which is 1) such that 2Z × Z Divide 37 by 21 with the quotient as 1, providing the remainder = 37 - 21 × 1 = 37 - 21 = 16.Now, let's discover the decimal places after the quotient 11.Bring down 00 to the best 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 ideal of 22, uncover a digit Z (which is 7) such that 22Z × Z Divide 1600 by 227 with the quotient as 7, providing the remainder = 1600 - 227 × 7 = 1600 - 1589 = 11.Bring down 00 again. Repeat over actions for finding more decimal areas for the square root of 137.

Because of this, the square root of 137 by long division approach is 11.7 approx.


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Example 1: Solve the equation x2 − 137 = 0

Solution:

x2 - 137 = 0 i.e. x2 = 137x = ±√137Because the worth of the square root of 137 is 11.705,⇒ x = +√137 or -√137 = 11.705 or -11.705.


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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 pairmuch less and is not in the power of 2. Thus, 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 create of square root of 137 cannot be streamlined additionally.

If the Square Root of 137 is 11.705. Find the Value of the Square Root of 1.37.

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Let us reexisting √1.37 in p/q form i.e. √(137/100) = 1.37/10 = 1.170. Hence, the worth of √1.37 = 1.170

Is the number 137 a Perfect Square?

The number 137 is prime. This indicates that the square root of 137 cannot be expressed as a product of two equal integers. Because of this, the number 137 is not a perfect square.

Evaluate 9 plus 8 square root 137

The provided expression is 9 + 8 √137. We know that the square root of 137 is 11.705. As such, 9 + 8 √137 = 9 + 8 × 11.705 = 9 + 93.638 = 102.638