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### Exercise 5.4 class 8 solution -exercise preview

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# 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.

## What is Square Root of Decimals

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.

### Exercise 5.4 class 8 solution-square root of decimal numbers

To find the square root of a decimal number, we will follow the steps given below. Consider the number is 51.84

Step 1. We put bars on the integral part (here 51) of the number in the usual manner and place bars on the decimal part (here 84) on every pair of digits beginning with the first decimal place.

proceed as usual, we get 51.84

Step 2. Now proceed in similar manner. The left most bar is 51 and 7^2<51<8^2, take 7 as divisor and the number under the left most bar as the divided i.e. 51

Divide and get the remainder

Step 3. The remainder is 2. Write the number under the next bar (i.e. 84) to the right of remainder, we get 284

Step 4. Double the quotient (ie. 7) and enter a blank on its right. Since 84 is the decimal part so put a decimal point in the quotient i e after 7

Step 5. We know 142 x2=284, So the new digit is 2, Divide and get

the remainder

Step 6. Since the remainder is zero and no bar left, therefore √51.84

= 7.2

Example –

### Exercise 5.4 class 8 solution – solution pdf

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DocScanner-5.4### 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:**5.5^{2}= 30.25 and 6^{2}= 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.

NCERT solutions for class 8 Maths exercise 1.1 chapter 1 (free Pdf download)