Square Root of Decimals: Square root of a decimal is similar to square root of an integer. Whereas, It examines practical uses for the knowledge of square roots of decimals, such as interest rate calculations in finance, distance and velocity calculations in physics, and other measurements and dimensions. Even, A number’s square root is the number multiplied by itself to get the original number, but a number’s square is the value of the number raised to the power of two. For example 5.657 × 5.657 = 32.
In this article, we will read about the square roots of decimals, how to find the square roots, and some examples.
What is Square Root of Decimals?
Square root of a decimal number is a value that is multiplied by itself to equal the specified decimal. Thus, square roots of decimals are often irrational numbers which means they cannot be expressed as fractions.
- In decimal form, √(45) = 6.708
- In fractional exponent form, (45)1/2 = 6.708
How to Find Square Root of Decimals?
To find the square root of decimals we can use the methods that are given below;
- Square Root by Estimation Method
- Square Root by Long Division Method
Square Root by Estimation Method
Square root of a given number can also be estimated and approximated using this method. To obtain the estimated square root value of a given decimal number, all we have to do is discover the perfect square numbers that are closest to it. So, to find it out we have to follow some steps;
Step 1: Firstly, find the greatest perfect square that is equal to or less than the specified amount.
Step 2: Then, to find the remaining decimal part, subtract the square of the whole number from the provided number.
Step 3: After that, for the needed approximate value, you will compare the decimal portion with the squares of successive decimal values.
Step 4: Lastly, Add the whole number component and the decimal approximation. Then, you get the estimated square root of the given number.
For example: Find the square root of 5.76
Finding perfect square close to 5.76. 4 and 9 are
This implies that √(5.76) lies between 2 and 3.
Now, we have to check if √(5.76) is closer to 2 or 3. Let 2 and 2.5.
5.76 is closer to 6.25
Therefore, approximate square root of 5.76 is 2.5
Square Root of Decimals by Long Division Method
Long Division method divides a division problem into a series of simpler steps and is primarily utilized when we need to divide huge numbers into steps or parts with their techniques. So, to find it out we have to follow some steps;
Step 1: Place a bar on a pair of digits.
Step 2: Then, Divide the number into pairs of digits, starting from the decimal point and moving left.
Step 3: After that, find the biggest digit that won’t exceed the current dividend when squared and multiplied by the divisor.
Step 4: To get the result, subtract the dividend from the current divisor, add the quotient to the result, and then divide the dividend by the current divisor. Then add a placeholder and twice the result.
Step 5: Repeat it until you get the approximate value, you want to reach.
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For example: Lets find square root of 1.125 by using the Long division method.
Step 1: Place a bar over every pair of digits above the numbers 1, 12, and 50.
Step 2: We divide 1 by 1 as 1 × 1 = 1. So, the quotient is 1 and the remainder is 0.
Step 3: Then, bring down the number under the next bar, which is 12.
Step 4: Add the last digit of the quotient to the divisor, 2. To the right of 2, write 0 as writing 1 will make it 21, and 21 is greater than 12. Now, the new divisor is 20.
Step 5: Add a decimal after 1 in the quotient.
Step 6: Since 12 is less than 20, bring down the next pair of numbers. Now the dividend is 1250.
Step 7: Now, to the right of 20, write 6 as 206 × 6 = 1236, which is smaller than 1250. Now again the new divisor is 206.
Step 8: Continue this process in the same way.
Thus, √(1.125) = 1.06
Square Root of Decimals Solved Examples
Example 1: What is the square root of 8.41?
Solution:
Square root of 8.41 is written as (8.41)1/2
(8.41)1/2 = (2.9 × 2.9)1/2
(8.41)1/2 = [(2.9)2]1/2
(8.41)1/2 = (2.9)2/2
(8.41)1/2 = (2.9)1
Therefore, √8.41 = 2.9
Example 2: What is the square root of 2.25?
Solution:
Square root of 2.25 can be written as (2.25)1/2
(2.25)1/2 = (1.5 × 1.5)1/2
(2.25)1/2 = [(1.5)2]1/2
(2.25)1/2 = (1.5)2/2
(2.25)1/2 = (1.5)1
Therefore , √2.25 = 1.5
Example 3: What is the square root of 1.142 by the long division method?
Solution:
- Step 1: Place a bar over every pair of digits above the numbers 1, 14, and 20.
- Step 2: We divide 1 by 1 as 1 × 1 = 1. So, the quotient is 1 and the remainder is 0.
- Step 3: Then, bring down the number under the next bar, which is 14.
- Step 4: Add the last digit of the quotient to the divisor, 1. To the right of 1, write 0. Now, the new divisor is 10.
- Step 5: Add decimal after 1 is the quotient.
- Step 6: Since 14 is less than 100, bring down the next pair of numbers. Now the dividend is 142.
- Step 7: Now, to the right of 10, write 3 as 103 × 3 = 309, which is smaller than 142. Now again with the new divisor is 103.
- Step 8: Continue this process in the same way. Until you get the approximate value in 1.068.
Square Root of Decimals WorkSheet
Q1: What is the square root of 5.76?
Q2: Find the square root of 12.96.
Q3: Calculate the square root of 0.81.
Q4: Determine the square root of 16.25.
Q5: What is the square root of 3.24?
FAQs on Square Root of Decimals
What is the square root of a decimal number?
A value that produces the original decimal number when multiplied by itself is known as the square root of a decimal number.
Can square root of a decimal be irrational?
Yes, It is possible for a decimal’s square root to be irrational, which means that it cannot be stated as a finite fraction or decimal.
What methods are used to find square root of a decimal number?
Methods that is used to find the square root of decimal number are:
- Square Root by Estimation Method
- Square Root by Long Division Method
How to find square root of decimals by estimation?
To get square root of decimals by estimation, is used to determine the entire number component and estimate the decimal part using the nearest perfect squares. Now, get an approximate square root, add these estimates together.
Which method is used to find square root of non-perfect square numbers?
Square root of a non-perfect square number is calculated by using long division method.
What are applications of square root of decimals?
Various applications of square root of decimals are:
- Used in algebra and geometry.
- Used in finding area and volumes of various shapes.
- Used by engineering.
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