Square root of decimal number :[Procedure ,examples and practice problem}

In this post, we’re going to learn to “find the square root of decimal numbers using the long division method”.So, till now we have learned to find square root using factorization,one tens method, and long division method. If you didn’t read these stuff, check now 

Today we’ll learn the complete concept of finding the square root of decimal numbers using the long division method. For that, we first going to discuss the procedure(step-by-step process) then solve some examples and at the end, there are practice problems for you.So, don’t forget to check out 

Procedure: 

Let’s take 147.1369 as an example and try to find its square root.

Step:01 Make pairs of digits from right to left in an integral part and left to right in the decimal part.

                      What is an integral part?                     What is the decimal part?
The Part that occurs before the decimal point is called the Integral part. The number occurs after the decimal point is called the decimal part.
Ex. In 147.1369, we have 147 as an integral part  Ex.In 147.1369,we have 1369 as a decimal part 

So, in the integral part, we form pairs from right to left side whereas in the decimal part we do the same process from left to right side.

Square root of decimal number

Step:02 If the number of digits in the decimal part is odd, then add one zero toward the right side of the decimal part.(By the way, this rule is not applicable in the given example ) .We will see it in another example 

Step:03 Find square root using long division method, as we’re finding the square root of perfect squares 

Square root of 147.1369

Step:04 You can put as many zeros you want to calculate decimal value up to the desired number of places.

Let’s see some examples to understand this concept in a better way 

Examples 

Q.1 Find the square root of 5.756 using the long division method 

Solution: 

Step: 01 Form pairs in the integral part as well as in the decimal part according to the rule. (see Step: 1 of procedure) 

Square root of decimal number

Step:02 Since, it has the odd number of digits in the decimal part i.e 756. So we will add one more zero add the end to make the calculation easier.

Square root of 5.7560

Step: 03 Calculate square root using the long division method up to the desired number of places. The most appropriate decimal place is up to two decimal places (If desired places are not given in the question

Square root of 5.7560 using long division method

Q.2 Find the square root using 321.7302 correct up to two decimal places of decimals 

Solution: 

Step: 01 Form the pair in the integral part as well as in the decimal part according to rule 

Step:02 Since, it has even numbers of digits in the decimal part i.e 7302. So, we don’t need to add extra zeroes 

Step: 03 In the problem, we have asked to calculate square root up to decimal places .so we will add zeroes at the end of the decimal part. We have to find up to three decimal places 

Step:04 Calculate value using long division method 

Square root of 321.7302

Q.3 Find the square of 0.5929 using the long division process 

Solution: 

Square root of 5929 using long division method

Q.4 Find the square of root of 86.71 upto two decimal places 

Solution: Square root of 86.71

Practice problem

Q.1 Find the square root of following numbers 

(i) 1.4161 

Answer: 1.19

(ii) 0.000625 

Answer: 0.025

(iii) 20.8849 

Answer: 4.56 

(iv) 0.64 

Answer: 0.08

(v) 3696.64 

Answer: 60.8

(vi) 2851.56 

Answer: 53.4

(vii) 331.24 

Answer: 18.2

(viii) 4277.16

Answer: 65.4

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