Square Root of Decimals

Square root of decimals is carried out in the same way as for whole numbers. Square root of a number and squaring a number are inverse operations. The Square of a number is the value of power 2 of the number, while the square root of a number is the number that is multiplied by itself to give the original number.

In this article, let's learn how to find the square root of decimals using solved examples and practice questions.

Square root of decimal is the value of a decimal number to the power 1/2. For example, the square root of 24.01 is 4.9 as (4.9)² = 24.01. The square root of a decimal number can be calculated by using the estimation method or the long division method.

In the case of long division method, the pairs of whole number parts and fractional parts are separated by using bars. And then, the process of long division is carried out in the same way as any other whole number.

Square Root by Estimation Method

Estimation and approximation is a reasonable guess of the actual value so as to make calculations easier and realistic. This method also helps in estimating and approximating the square root of a given number. We just need to find the nearest perfect square numbers to the given decimal number to find its approximate square root value.

Let's find the square root of 31.36.

• Step 1: Find the nearest perfect square numbers to 31.36. 25 and 36 are the perfect square numbers nearest to 31.36.
• Step 2: √25 = 5 and √36 = 6. This implies that √31.36 lies between 5 and 6.
• Step 3: Now, we need to see if √31.36 is closer to 5 or 6. Let us consider 5.5 and 6.
• Step 4: 5.5² = 30.25 and 6²= 36. Thus, √31.36 lies between 5.5 and 6 and is closer to 5.5.

Thus, the square root of 31.36 is close to 5.5.

Square Root by Long Division Method

Long Division method is mainly used in case we need to dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. We can find the exact square root of any given number using this method. Let us understand the process step by step, with an example. Let's find the square root of 2.56.

• Step 1: Place a bar over every pair of digits of the given decimal number starting from the unit’s place. We will have two pairs, i.e. 2 and 56.
• Step 2: We start with the whole number part and divide it by the largest number whose square is less than or equal to that number. Here, the whole number part is 2 and we have 1 x 1 = 1. So, the quotient is 1.

• Step 3: Bring down the number, that is the pair of the fractional parts under the next bar to the right of the remainder(that is 1).
• Step 4: Add the last digit of the quotient to the divisor, which is 1 + 1 = 2. To the right of the obtained sum( that is 2), find a suitable number that, together with the result of the sum, forms a new divisor for the new dividend (that is, 156) that is carried down. Also, add decimal after 1 in the quotient as we move to the fractional part.

• Step 5: The new number in the quotient will have the same number as selected in the divisor, thus the divisor will now be 26 and the quotient will be 1.6, as 26 x 6 = 156. (The condition is the same — as being either less than or equal to the dividend).
• Step 6: Continue this process further using a decimal point and adding zeros in pairs to the remainder.

• Step 6: The quotient thus obtained will be the square root of the number. Thus, the square root of 2.56 is 1.6.

Related Articles on Square Root of Decimals:

Given below is the list of topics that are closely connected to the square root of decimals.

• Square Root Formula
• Square Root Calculator
• Square Roots Worksheets

What Is the Square Root of Decimals in Math?

Square root of decimals refers to the value of a decimal number to the power 1/2. For example, the square root of 12.25 is 3.5 as (3.5)² = 12.25. It is calculated by estimation as well as long division method. It is easy to find the exact square root of any given number using the long division method.

Which Method is Used to Find the Square Root of Non-Perfect Square Numbers?

In Math, a non-perfect number is considered the one that is in decimal form. The square root of a non-perfect square number can be calculated by using the long division method.

What are the Applications of the Square Root of Decimals?

There are various applications of the square root of decimals.

• Used in algebra and geometry. It helps in finding the roots of a quadratic equation.
• Make calculations for the area, volume, and other measurements easy.
• Widely used by engineers.

How To Find Square Root of Decimals by Estimation?

To find the square root of decimals by estimation, look for the perfect square numbers close to the given decimal numbers. Find their square roots to have an approximate value for the square root of the given decimal number. For example, the square root of 11.56 is 3.4.

• Step 1: √11.56 is close to the perfect squares, 9 and 16.
• Step 2: √9 = 3 and √16 = 4.
• Step 3: Check for 3.5². 3.5² = 12.25. This implies √11 lies between 3 and 3.5.

What Are the Steps to Find Square Root of Decimals by Long Division Method?

• Step 1: Place a bar over every pair of digits of the number, whole number part as well as fractional part.
• Step 2: Divide the left-most number, the whole number part by the largest number whose square is less than or equal to the number in the left-most pair.
• Step 3: Bring down the number under the next bar to the right of the remainder. Add the last digit of the quotient to the divisor. To the right of the obtained sum, find a suitable number which, together with the result of the sum, forms a new divisor for the new dividend that is carried down.
• Step 4: The new number in the quotient will have the same number as selected in the divisor. The condition is the same — as being either less than or equal to the dividend.
• Step 5: Then, continue this process further using a decimal point and adding zeros in pairs to the remainder.
• Step 6: The quotient thus obtained will be the square root of the given decimal number.