Square root of 192

In this article, the square root of 192 is ±13.454. The square root of 192 is expressed as √192, in radical form. It is expressed as (192)^½ in exponential form.
 

If a student wants to find the square root of a number. Which are the methods they can use?  Some common methods are,

• Prime factorization

• Long division

• Approximation

• Subtraction method

Let’s check the square root of 192 using these methods 
 

In this method, all the prime factors of the number are listed down and then from there one number from each pair is listed down. Then the numbers are multiplied together. 

By using prime factorization, let’s check out the square root of 192.

Step 1: Listing out the prime factors of 192 and pairing the same numbers.

Prime factors of 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

 
Pairing the factors, i.e, (2 × 2) × (2 × 2) × (2 × 2) × 3  

Step 2: multiplying a number from each pair

2 × 2 × 2 ×√3= 8√3

Hence, the √192 is 8√3
 

Here, the given number is divided into smaller numbers to find the square root of the number.

Using the long division method, let’s check the square root of 192

Step 1: The number given, 192 has three digits so let’s pair that number. Here it is 1 and 75.

Finding the number whose square is less than or equal to the 1

 Here the number is, because 1² = 1

Step 2: So, let’s divide 1 by 1

Step 3: Now, the quotient and divisor is 1, for the new divisor we add the divisor with itself.

Step 4: Continue the process till the remainder is 0

The quotient will be the square root of the number.

Therefore, the square root of 192 is ±13.856

In the subtraction method, based on the fact, the sum of the first n odd number is n2. So, here the given number is subtracted with the odd number starting with 1. The process will go on till the given number becomes 0. The method is mainly used for perfect squares; it is not used to find the square root of 192.
 

• Quotient: The result we got after dividing two numbers is the quotient

• Radical symbol: The radical symbol (√) is the symbol used to denote square root.

• Square of a number: The Square of a number is the product of the number when multiplied by itself.

• Prime factorization: It is the process of breaking down a number into prime numbers.