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 x² = 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

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

• 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.

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 = 2² × 31
• Finally, to find the root of this from here it is very easy,
  √124 = √(2² × 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

• Square Root of 125
• Square Root of 123
• Square Root of 120
• Square Root of 121
• Square Root of 1024

• 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.

• 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?