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Square Root of 114

The square root of 114 is expressed as √114 in the radical form and as (114)^½ or (114)^0.5 in the exponent form. The square root of 114 rounded up to 9 decimal places is 10.677078252. It is the positive solution of the equation x² = 114.

Square Root of 114: 10.677078252031311
Square Root of 114 in exponential form: (114)^½ or (114)^0.5
Square Root of 114 in radical form: √114

Square Root of 114

1.	What is the Square Root of 114?
2.	How to find the Square Root of 114?
3.	Is the Square Root of 114 Irrational?
4.	FAQs

What is the Square Root of 114?

The square root of 114, (or root 114), is the number which when multiplied by itself gives the product as 114. Therefore, the square root of 114 = √114 = 10.677078252031311.

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How to Find Square Root of 114?

Square Root of 114 by Long Division Method

Value of √114 by Long Division Method

Explanation:

Forming pairs: 01 and 14
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 14, to the right of the remainder 0. The new dividend is now 14.
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 0) such that 2Z × Z <= 14. After finding Z, together 2 and Z (0) form a new divisor 20 for the new dividend 14.
Divide 14 by 20 with the quotient as 0, giving the remainder = 14 - 20 × 0 = 14 - 0 = 14.
Now, let's find the decimal places after the quotient 10.
Bring down 00 to the right of this remainder 14. The new dividend is now 1400.
Add the last digit of quotient to divisor i.e. 0 + 20 = 20. To the right of 20, find a digit Z (which is 6) such that 20Z × Z <= 1400. Together they form a new divisor (206) for the new dividend (1400).
Divide 1400 by 206 with the quotient as 6, giving the remainder = 1400 - 206 × 6 = 1400 - 1236 = 164.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 114.

Therefore, the square root of 114 by long division method is 10.6 approximately.

Is Square Root of 114 Irrational?

The actual value of √114 is undetermined. The value of √114 up to 25 decimal places is 10.67707825203131121081152. Hence, the square root of 114 is an irrational number.

☛ Also Check:

Square Root of 69 - √69 = 8.30662
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Square Root of 37 - √37 = 6.08276
Square Root of 74 - √74 = 8.60233
Square Root of 99 - √99 = 9.94987
Square Root of 29 - √29 = 5.38516
Square Root of 8 - √8 = 2.82843

Square Root of 114 Solved Examples

Example 1: Solve the equation x² − 114 = 0

Solution:

x² - 114 = 0 i.e. x² = 114
x = ±√114
Since the value of the square root of 114 is 10.677,
⇒ x = +√114 or -√114 = 10.677 or -10.677.
Example 2: If the area of an equilateral triangle is 114√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 114√3 in²
⇒ a = ±√456 in
Since length can't be negative,
⇒ a = √456 = 2 √114
We know that the square root of 114 is 10.677.
⇒ a = 21.354 in
Example 3: If the area of a circle is 114π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 114π in²
⇒ r = ±√114 in
Since radius can't be negative,
⇒ r = √114
The square root of 114 is 10.677.
⇒ r = 10.677 in

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FAQs on the Square Root of 114

What is the Value of the Square Root of 114?

The square root of 114 is 10.67707.

Why is the Square Root of 114 an Irrational Number?

Upon prime factorizing 114 i.e. 2¹ × 3¹ × 19¹, 2 is in odd power. Therefore, the square root of 114 is irrational.

What is the Value of 3 square root 114?

The square root of 114 is 10.677. Therefore, 3 √114 = 3 × 10.677 = 32.031.

If the Square Root of 114 is 10.677. Find the Value of the Square Root of 1.14.

Let us represent √1.14 in p/q form i.e. √(114/100) = 1.14/10 = 1.068. Hence, the value of √1.14 = 1.068

Evaluate 14 plus 17 square root 114

The given expression is 14 + 17 √114. We know that the square root of 114 is 10.677. Therefore, 14 + 17 √114 = 14 + 17 × 10.677 = 14 + 181.510 = 195.510

Is the number 114 a Perfect Square?

The prime factorization of 114 = 2¹ × 3¹ × 19¹. Here, the prime factor 2 is not in the pair. Therefore, 114 is not a perfect square.

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