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Square Root of 134

The square root of 134 is expressed as √134 in the radical form and as (134)^½ or (134)^0.5 in the exponent form. The square root of 134 rounded up to 8 decimal places is 11.57583690. It is the positive solution of the equation x² = 134.

Square Root of 134: 11.575836902790225
Square Root of 134 in exponential form: (134)^½ or (134)^0.5
Square Root of 134 in radical form: √134

Square Root of 134

1.	What is the Square Root of 134?
2.	How to find the Square Root of 134?
3.	Is the Square Root of 134 Irrational?
4.	FAQs

What is the Square Root of 134?

The square root of 134, (or root 134), is the number which when multiplied by itself gives the product as 134. Therefore, the square root of 134 = √134 = 11.575836902790225.

☛ Check: Square Root Calculator

How to Find Square Root of 134?

Square Root of 134 by Long Division Method

Value of √134 by Long Division Method

Explanation:

Forming pairs: 01 and 34
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 34, to the right of the remainder 0. The new dividend is now 34.
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 <= 34. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 34.
Divide 34 by 21 with the quotient as 1, giving the remainder = 34 - 21 × 1 = 34 - 21 = 13.
Now, let's find the decimal places after the quotient 11.
Bring down 00 to the right of this remainder 13. The new dividend is now 1300.
Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 5) such that 22Z × Z <= 1300. Together they form a new divisor (225) for the new dividend (1300).
Divide 1300 by 225 with the quotient as 5, giving the remainder = 1300 - 225 × 5 = 1300 - 1125 = 175.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 134.

Therefore, the square root of 134 by long division method is 11.5 approx.

Is Square Root of 134 Irrational?

The actual value of √134 is undetermined. The value of √134 up to 25 decimal places is 11.57583690279022547355581. Hence, the square root of 134 is an irrational number.

☛ Also Check:

Square Root of 1681 - √1681 = 41
Square Root of 99 - √99 = 9.94987
Square Root of 33 - √33 = 5.74456
Square Root of 841 - √841 = 29
Square Root of 289 - √289 = 17
Square Root of 149 - √149 = 12.20656
Square Root of 116 - √116 = 10.77033

Square Root of 134 Solved Examples

Example 1: Solve the equation x² − 134 = 0

Solution:

x² - 134 = 0 i.e. x² = 134
x = ±√134
Since the value of the square root of 134 is 11.576,
⇒ x = +√134 or -√134 = 11.576 or -11.576.
Example 2: If the area of a circle is 134π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 134π in²
⇒ r = ±√134 in
Since radius can't be negative,
⇒ r = √134
The square root of 134 is 11.576.
⇒ r = 11.576 in
Example 3: If the surface area of a sphere is 536π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 536π in²
⇒ r = ±√134 in
Since radius can't be negative,
⇒ r = √134
The square root of 134 is 11.576.
⇒ r = 11.576 in

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FAQs on the Square Root of 134

What is the Value of the Square Root of 134?

The square root of 134 is 11.57583.

Why is the Square Root of 134 an Irrational Number?

Upon prime factorizing 134 i.e. 2¹ × 67¹, 2 is in odd power. Therefore, the square root of 134 is irrational.

What is the Value of 16 square root 134?

The square root of 134 is 11.576. Therefore, 16 √134 = 16 × 11.576 = 185.213.

What is the Square Root of -134?

The square root of -134 is an imaginary number. It can be written as √-134 = √-1 × √134 = i √134 = 11.575i
where i = √-1 and it is called the imaginary unit.

Evaluate 13 plus 17 square root 134

The given expression is 13 + 17 √134. We know that the square root of 134 is 11.576. Therefore, 13 + 17 √134 = 13 + 17 × 11.576 = 13 + 196.789 = 209.789

Is the number 134 a Perfect Square?

The prime factorization of 134 = 2¹ × 67¹. Here, the prime factor 2 is not in the pair. Therefore, 134 is not a perfect square.

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