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.

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

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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

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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Value of √122 by Long Division Method

Explanation:

Forming pairs: 01 and 22Find a number Y (1) such that whose square is 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 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 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.


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Example 1: Solve the equation x2 − 122 = 0

Solution:

x2 - 122 = 0 i.e. x2 = 122x = ±√122Since the value of the square root of 122 is 11.045,⇒ x = +√122 or -√122 = 11.045 or -11.045.


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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 = 11.045iwhere i = √-1 and it is called the imaginary unit.

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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