Square Root of 124
The square root of 124 is expressed as √124 in the radical form and as (124)^{½} or (124)^{0.5} in the exponent form. The square root of 124 rounded up to 9 decimal places is 11.135528726. It is the positive solution of the equation x^{2} = 124. We can express the square root of 124 in its lowest radical form as 2 √31.
 Square Root of 124: 11.135528725660043
 Square Root of 124 in exponential form: (124)^{½} or (124)^{0.5}
 Square Root of 124 in radical form: √124 or 2 √31
1.  What is the Square Root of 124? 
2.  Is Square Root of 124 Rational or Irrational? 
3.  How to Find the Square Root of 124? 
4.  FAQs on Square Root of 124 
What is the Square Root of 124?
The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 124 can be written in multiple ways
 Radical form: √124
 Decimal form: 11.135
 Exponent form: (124)^{1/2}
Is Square Root of 124 Rational or Irrational?
 124 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
 Also, its square root cannot be expressed as a fraction of the form p/q which confirms to us that the square root of 124 is an irrational number.
How to Find the Square Root of 124?
There are multiple ways to find the square root of 124
 Long Division
 Prime Factorization
 Estimation and Approximation
Long Division Method
The square root of 124 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 124 by putting a bar above 24 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied by itself, gives a product less than or equal to 1. This will be 1 obviously, so place 1 in the quotient and the divisors place which will result in the remainder being 0.
 Step 3: Drag down 24 beside the remainder 0. Also, add the divisor to itself and write it below.(1+1=2)
 Step 3: Find a number X such that 2X × X results in a number less than or equal to 24. The number 1 fits here so fill it next to 1 in the divisor as well as next to 1 in the quotient.
 Step 4: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding, X to the divisor, the new divisor becomes 22.
 Step 5: Repeat this process to get the decimal places you want.
Therefore, the square root of 124 = 11.135
Prime Factorization
 To find the square root of 124, we shall first express it in terms of its prime factors.
124 = 2 × 2 × 31  Next, this can be reduced further to
124 = 2^{2} × 31  Finally, to find the root of this from here it is very easy,
√124 = √(2^{2} × 31)
√124 = 2√31 = 11. 135
Therefore, the Square Root of 124 ≅ 11.135.
However, one must note that this method is not the most convenient to use as it involves finding the square root of 31 which is not commonly known.
Explore Square roots using illustrations and interactive examples
Important Notes
 There exists a positive and negative root of 124, 11.135 and 11.135.
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits.
Challenging Questions
 What is the square root of 124 up to 6 decimal places(Use Long Division)?
 Is 11.135 a root of 124? If yes, why?
Solved Examples

Example 1: What is the square root of √124?
Solution:
The square root of negative numbers is represented by imaginary numbers.
So, the square root of √124 is written as √124 i. Where (i = √1) 
Example 2: Charles has a cube. The area of all 6 sides of the cube is 744 mm^{2}. Help him calculate the edge length of the cube.
Solution:
Total Surface Area is 744 mm^{2}
Surface Area of each side = 744/6 = 124 mm^{2}
Edge Length = √124 = 11.135
Therefore, the edge length of the cube is 11.135 cm. 
Example: Solve the equation x^{2} − 124 = 0
Solution:
x^{2}  124 = 0 i.e. x^{2} = 124
x = ±√124
Since the value of the square root of 124 is 11.136,
⇒ x = +√124 or √124 = 11.136 or 11.136.
FAQs on the Square Root of 124
What is the Value of the Square Root of 124?
The square root of 124 is 11.13552.
Why is the Square Root of 124 an Irrational Number?
Upon prime factorizing 124 i.e. 2^{2} × 31^{1}, 31 is in odd power. Therefore, the square root of 124 is irrational.
What is the Square Root of 124 in Simplest Radical Form?
We need to express 124 as the product of its prime factors i.e. 124 = 2 × 2 × 31. Therefore, √124 = √2 × 2 × 31 = 2 √31. Thus, the square root of 124 in the lowest radical form is 2 √31.
What is the Value of 6 square root 124?
The square root of 124 is 11.136. Therefore, 6 √124 = 6 × 11.136 = 66.813.
Is the number 124 a Perfect Square?
The prime factorization of 124 = 2^{2} × 31^{1}. Here, the prime factor 31 is not in the pair. Therefore, 124 is not a perfect square.
Evaluate 15 plus 16 square root 124
The given expression is 15 + 16 √124. We know that the square root of 124 is 11.136. Therefore, 15 + 16 √124 = 15 + 16 × 11.136 = 15 + 178.168 = 193.168
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