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Square Root of 122

The square root of 122 is expressed as √122 in the radical form and as (122)^½ or (122)^0.5 in the exponent form. The square root of 122 rounded up to 7 decimal places is 11.0453610. It is the positive solution of the equation x² = 122.

Square Root of 122: 11.045361017187261
Square Root of 122 in exponential form: (122)^½ or (122)^0.5
Square Root of 122 in radical form: √122

Square Root of 122

1.	What is the Square Root of 122?
2.	How to find the Square Root of 122?
3.	Is the Square Root of 122 Irrational?
4.	FAQs

What is the Square Root of 122?

The square root of 122, (or root 122), is the number which when multiplied by itself gives the product as 122. Therefore, the square root of 122 = √122 = 11.045361017187261.

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How to Find Square Root of 122?

Square Root of 122 by Long Division Method

Value of √122 by Long Division Method

Explanation:

Forming pairs: 01 and 22
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 22, to the right of the remainder 0. The new dividend is now 22.
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 <= 22. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 22.
Divide 22 by 21 with the quotient as 1, giving the remainder = 22 - 21 × 1 = 22 - 21 = 1.
Now, let's find the decimal places after the quotient 11.
Bring down 00 to the right of this remainder 1. The new dividend is now 100.
Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 0) such that 22Z × Z <= 100. Together they form a new divisor (220) for the new dividend (100).
Divide 100 by 220 with the quotient as 0, giving the remainder = 100 - 220 × 0 = 100 - 0 = 100.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 122.

Therefore, the square root of 122 by long division method is 11.0 approximately.

Is Square Root of 122 Irrational?

The actual value of √122 is undetermined. The value of √122 up to 25 decimal places is 11.04536101718726077421091. Hence, the square root of 122 is an irrational number.

☛ Also Check:

Square Root of 23 - √23 = 4.79583
Square Root of 26 - √26 = 5.09902
Square Root of 42 - √42 = 6.48074
Square Root of 116 - √116 = 10.77033
Square Root of 15 - √15 = 3.87298
Square Root of 27 - √27 = 5.19615
Square Root of 56 - √56 = 7.48331

Square Root of 122 Solved Examples

Example 1: Solve the equation x² − 122 = 0

Solution:

x² - 122 = 0 i.e. x² = 122
x = ±√122
Since the value of the square root of 122 is 11.045,
⇒ x = +√122 or -√122 = 11.045 or -11.045.
Example 2: If the area of an equilateral triangle is 122√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 = 122√3 in²
⇒ a = ±√488 in
Since length can't be negative,
⇒ a = √488 = 2 √122
We know that the square root of 122 is 11.045.
⇒ a = 22.091 in
Example 3: If the surface area of a sphere is 488π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 488π in²
⇒ r = ±√122 in
Since radius can't be negative,
⇒ r = √122
The square root of 122 is 11.045.
⇒ r = 11.045 in

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FAQs on the Square Root of 122

What is the Value of the Square Root of 122?

The square root of 122 is 11.04536.

Why is the Square Root of 122 an Irrational Number?

Upon prime factorizing 122 i.e. 2¹ × 61¹, 2 is in odd power. Therefore, the square root of 122 is irrational.

What is the Square Root of -122?

The square root of -122 is an imaginary number. It can be written as √-122 = √-1 × √122 = i √122 = 11.045i
where i = √-1 and it is called the imaginary unit.

Evaluate 3 plus 6 square root 122

The given expression is 3 + 6 √122. We know that the square root of 122 is 11.045. Therefore, 3 + 6 √122 = 3 + 6 × 11.045 = 3 + 66.272 = 69.272

Is the number 122 a Perfect Square?

The prime factorization of 122 = 2¹ × 61¹. Here, the prime factor 2 is not in the pair. Therefore, 122 is not a perfect square.

What is the Square Root of 122 in Simplest Radical Form?

We need to express 122 as the product of its prime factors i.e. 122 = 2 × 61. Therefore, as visible, the radical form of the square root of 122 cannot be simplified further. Therefore, the simplest radical form of the square root of 122 can be written as √122

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