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Square Root of 111

The square root of 111 is expressed as √111 in the radical form and as (111)^½ or (111)^0.5 in the exponent form. The square root of 111 rounded up to 8 decimal places is 10.53565375. It is the positive solution of the equation x² = 111.

Square Root of 111: 10.535653752852738
Square Root of 111 in exponential form: (111)^½ or (111)^0.5
Square Root of 111 in radical form: √111

Square Root of 111

1.	What is the Square Root of 111?
2.	How to find the Square Root of 111?
3.	Is the Square Root of 111 Irrational?
4.	FAQs

What is the Square Root of 111?

The square root of 111, (or root 111), is the number which when multiplied by itself gives the product as 111. Therefore, the square root of 111 = √111 = 10.535653752852738.

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How to Find Square Root of 111?

Square Root of 111 by Long Division Method

Value of √111 by Long Division Method

Explanation:

Forming pairs: 01 and 11
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 11, to the right of the remainder 0. The new dividend is now 11.
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 <= 11. After finding Z, together 2 and Z (0) form a new divisor 20 for the new dividend 11.
Divide 11 by 20 with the quotient as 0, giving the remainder = 11 - 20 × 0 = 11 - 0 = 11.
Now, let's find the decimal places after the quotient 10.
Bring down 00 to the right of this remainder 11. The new dividend is now 1100.
Add the last digit of quotient to divisor i.e. 0 + 20 = 20. To the right of 20, find a digit Z (which is 5) such that 20Z × Z <= 1100. Together they form a new divisor (205) for the new dividend (1100).
Divide 1100 by 205 with the quotient as 5, giving the remainder = 1100 - 205 × 5 = 1100 - 1025 = 75.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 111.

Therefore, the square root of 111 by long division method is 10.5 approximately.

Is Square Root of 111 Irrational?

The actual value of √111 is undetermined. The value of √111 up to 25 decimal places is 10.53565375285273884840140. Hence, the square root of 111 is an irrational number.

☛ Also Check:

Square Root of 25 - √25 = 5
Square Root of 11 - √11 = 3.31662
Square Root of 61 - √61 = 7.81025
Square Root of 320 - √320 = 17.88854
Square Root of 40 - √40 = 6.32456
Square Root of 16 - √16 = 4
Square Root of 125 - √125 = 11.18034

Square Root of 111 Solved Examples

Example 1: Solve the equation x² − 111 = 0

Solution:

x² - 111 = 0 i.e. x² = 111
x = ±√111
Since the value of the square root of 111 is 10.536,
⇒ x = +√111 or -√111 = 10.536 or -10.536.
Example 2: If the surface area of a sphere is 444π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 444π in²
⇒ r = ±√111 in
Since radius can't be negative,
⇒ r = √111
The square root of 111 is 10.536.
⇒ r = 10.536 in
Example 3: If the area of an equilateral triangle is 111√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 = 111√3 in²
⇒ a = ±√444 in
Since length can't be negative,
⇒ a = √444 = 2 √111
We know that the square root of 111 is 10.536.
⇒ a = 21.071 in

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FAQs on the Square Root of 111

What is the Value of the Square Root of 111?

The square root of 111 is 10.53565.

Why is the Square Root of 111 an Irrational Number?

Upon prime factorizing 111 i.e. 3¹ × 37¹, 3 is in odd power. Therefore, the square root of 111 is irrational.

If the Square Root of 111 is 10.536. Find the Value of the Square Root of 1.11.

Let us represent √1.11 in p/q form i.e. √(111/100) = 1.11/10 = 1.054. Hence, the value of √1.11 = 1.054

Is the number 111 a Perfect Square?

The prime factorization of 111 = 3¹ × 37¹. Here, the prime factor 3 is not in the pair. Therefore, 111 is not a perfect square.

What is the Square Root of 111 in Simplest Radical Form?

We need to express 111 as the product of its prime factors i.e. 111 = 3 × 37. Therefore, as visible, the radical form of the square root of 111 cannot be simplified further. Therefore, the simplest radical form of the square root of 111 can be written as √111

Evaluate 4 plus 3 square root 111

The given expression is 4 + 3 √111. We know that the square root of 111 is 10.536. Therefore, 4 + 3 √111 = 4 + 3 × 10.536 = 4 + 31.607 = 35.607

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