Square Root of Decimal Number

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Introduction to Square Root

Any number can be expressed as the product of the prime numbers. This method of representation of a number in terms of the product of prime numbers is termed as the prime factorization method. It is the easiest method known for the manual calculation of the square root of decimal numbers. But this method becomes tedious and tiresome when the amount involved is large. In order to beat this problem we use the division method. 

 

Consider the following method for finding the square root of the decimal number. It is explained with the assistance of an example for a transparent understanding.

 

Note: The number of digits in a perfect square is very significant for calculating its square root of decimal number by long division method. 

 

What is Square Root of Decimal Number?

A Square root of a decimal number is a value that, when multiplied by itself, gives the number. The symbol it is represented by is √ which always is taken as the positive square root.

 

Steps for Finding the Square Root of Decimal Number

To find the square root of decimal number within the decimal form are explained within the following steps:

 

Step I: 

Make the total amount of the decimal places even just by affixing the zero on the acute right of the decimal part (only if required).

 

Step II: 

Inside an integral part, point out the periods as we do while finding the root of an ideal square of some number.

 

Step III: 

Inside the decimal part, point out the periods on every pair of the digits beginning with the primary decimal place.

 

Step IV: 

Now, find the square root of the decimal number by division method.

 

Step V: 

Put the percentage point within the root as soon because the integral part is exhausted.

 

Examples to be Solved 


Question 1: Find the Square Root of Decimal Number 29.16.

 

Solution: The following steps will explain finding the square root of decimal number 29.16 by using the long division method:

 

Step 1. Write down the decimal number and then make pairs of the integer and fractional parts separately. Then the pair of the integers of a decimal number is created from right to left and so the pair of the fractional part is made right from the start of the decimal point.

 

Example: Within the decimal number 29.16, 29 is one pair and then 16 is another pair.

 

Step 2. Find the amount whose pair is a smaller amount than or adequate to the primary pair. In the number 29.16, 5 squares is adequate to 25. Hence, we'll write 5 within the divisor and 5 within the quotient.

 

Step 3. Now, we will subtract 25 from 29. The answer is 4. We will bring down the opposite pair which is 16 and put the percentage point within the quotient.

 

Step 4. Now, we'll multiply the divisor by 2. Since 5 into 2 is adequate to 10, so we'll write 10 below the divisor. We need to seek out the third digit of the amount in order that it's completely divisible by the amount 416. We already have two digits 10. The 3rd digit should be 4 because 104 . 4 = 116.

 

Step 5. Write 4 in quotient's place. Hence, the answer is 5.4.

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Question 2: Find the square root of decimal number 84.64 by using a long division method.

 

Solution: Follow these steps to seek out the root of this decimal number 84.64.

 

Step 1. Write down the decimal number and then make pairs of the integer and fractional parts separately. The pair of the integers of a decimal number is made from right to left and so the pair of the fractional part is made right from the start of the decimal point.

So , in the decimal number 84.64, 84 is one pair and then 64 is another one.

 

Step 2. Find the amount whose pair is a smaller amount than or adequate to the primary pair. In the number 84.64, 9 squares is equal to 81. Hence, we'll write 9 within the divisor and 9 within the quotient.

 

Step 3. Now, we'll subtract 81 from 84. The answer is 3. We will bring down the opposite pair which is 64 and put the percentage point within the quotient after 9.

 

Step 4. Now, we'll multiply the divisor by 2. Since 9 into 2 is adequate to 18, so we'll write 18  below the divisor. We have to find out the third digit for the number so that it is totally divisible by the number 364. We already have two digits 18. The 3rd digit should be 2 because 182 . 2 = 364.

 

Step 5. Write 2 within the quotient's place after the percentage point . Hence, the answer is 9.2.

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FAQ (Frequently Asked Questions)

Question 1: What is the Formula of Square Root?

Answer: The square root of the number 'x' is written as √x. The square root of a number can be represented in exponential form as the number to the power ½. The square root of a number 'x' can be written in exponential form as (x)1/2.

Question 2: How do You Calculate a Square?

Answer: Multiply the length times the width to find the area. State your answer in square units. For example, if a room is 8 feet by 10 feet, then multiply it 8 times 10 to get the area of 80 square feet.

Question 3: What Numbers are a Perfect Square?

Answer: The perfect squares are the squares for the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 … Here are some square roots of all the perfect squares from 1 to 100. 1.  Firstly, get as much as close as you can by just finding out two perfect square roots and your number in between.

Question 4: What is the Square of 6400?

Answer: Square Root Table 1-100

 

Number

Square

Square Root

  80

6,400

  8.944

  81

6,561

  9.000

  82

6,724

  9.055

  83

6,889

  9.110