What is square Root? 

The square root is the number multiplied by itself to give the “original number.”The square root of a decimal number is done in a similar way to that for whole numbers. Let’s look at how to find the square root of a decimal number.

What is the square root of decimal numbers?

The square root of a decimal means the value of a “decimal number” to the power ½. For example, the square root of 40.96 is 6.4 when you multiply 6.4×6.4= 40.96. There are two common methods to find the square root of decimal numbers. We can use the long division method or estimation method. Let’s look at examples using these methods.

How to find the square root of decimal numbers

●        Square root by repeated subtraction

●        Square root by Prime factorization

Prime Factorization

This means representing the number as a product of prime numbers. Here’s is how to do it

Step 1: Find the prime factorization

Step 2: arrange the factors in similar pairs

Step 3: Use factor to represent the pair

Step 4: Find the product of the representatives

Step 5: The product is the square root.

For example: Find the square root of 0.81 using the Prime Factorization Method

Solution

Ignore the whole number and find the prime factorization of 81

The prime factors are

3 x 3 x 3 x 3

Arrange in similar pairs

(3 x 3) (3 x 3)

Pick one number in each pair and find its product

3 x 3 = 9

Therefore the square root of 81 is 9

Convert it back to a decimal

Therefore the square root of 0.81 is 0.9

Repeated Subtraction Method of Square Root

This simple method involves subtracting the “consecutive odd numbers” from the given number for finding the square root until 0. The square root of the number is the number of times we subtract. Moreover, this method works for perfect squares. Here is an example of finding square root using this method:

Example: Find The Square root of 0.36 using repeated subtraction method

Solution

Ignore the decimal and subtract repeatedly

36- 1 =35

35- 3 = 32

32- 5 = 27

27- 7 = 20

20 – 9 = 11

11 – 11 = 0

The square root of 0.36 is 0.6 since we have subtracted 36 by odd numbers 6 times