Square Root of 146

For non-perfect square numbers like 146 which are not perfect squares, there is no square root which will be a whole number and that will be some decimal value or irrational number.

The number which is multiply by itself to produce the square root of 146. 146 is NOT a perfect square, and thus the square root of 146 is not an exact whole number, the approximate value of √146 = 12.083

The square of a number is represented as x². 

In radical form, it is written as √146 and (146)^½ in exponential form. 

We can use three different methods to find the square root of 146

• Prime factorization method

• Long division method 

• Approximation method 
   

We apply this technique by factorizing the number into prime factors.

Step 1: Look for the prime factorization of 146

Prime factors of 146 is 2x73

Both 2 and 73 are prime numbers.

Now that we have all the factors and their product.

Step 2: Pair them(if possible).

But we cannot pair 146 as identical prime factors. Prime factorization will not help us simplify the square root of 146 in this case due to having no perfect square factors.

This implies that prime factorization on the non perfect-square like 146 does not yield clean form since it is already the most simplified form. For numbers that are not perfect squares, we have to use techniques like long division or estimation.

In the case of non-perfect squares we can use long division to get a more accurate decimal place.

• Step 1: Begin by pairing the digits of 146 from the right. As 146 has three numbers, consider "1" and "46" as combinations.

• Step 2: Pick the largest number which, when squared, results in a number less than or equal to (√1) group. That number is 1, as 1x1=1. 

• Step 3: Isolate the third group of zeros (42), Subtract 1 from 100, the result is remainder is 0. Then bring down the next two digits and append it to zero in the previous step.

• Step 4: Multiply the number (quotient) by 1 and write the product(2) as the next digit of the divisor.

• Step 5: Next, you have to Guess a digit (Let it be 2) which when placed next to 2 turns the number into a form that will result in the nearest whole number possible after multiplying by 2. Here, the digit is 2 as when we multiply 22 with 2 gives no remainder.

• Step 6: Repeat this process for more decimal places (e.g. 12.083) Therefore, the answer is square root of 146 is 12.083

This process estimate the square root of a number

Step 1: The first thing you need to do is identify the nearest perfect square to 146

So we can take 12 and 13. 

Step 2: We can guess that 146 is close to 122 which is 144, you we can approximate that the square root of 146 is a slight larger than 12. 

Step 3: Estime by calculating 

12x12=144

12.1x12.1=146.41

So now we have a close approximation that is the square root of 146 as 12.08



 

• Radicals — It is a symbol represented by √. In math, this symbol is used to represent the square root, cube root or fourth root of a number. 

• Repeated subtraction method — In this method, sequential odd numbers are subtracted from the number until the remainder becomes zero. 

• Radicand  — The number that is under the radical symbol is called radicand. So in √5, 5 is called radicand. 

• Square-In math, square and square root are different terms to explain different mathematical expressions. For a square of a number it is multiplied by the same number twice and square root is the inverse function of square. So square of 4 will be 4×4 = 16 but for square root of 16 it will be √16 = ±4