How to find square root of decimal number
Explain its method

Dear Student
​​​Here is the method to find square root of decimal numbers.

To find the square root of 51.84 by division method, we have to follow these steps:

Step 1

We place bars on the integral part of the decimal over every pair of digits starting from the digit at ones place and on the decimal part of the decimal number over every pair of digits starting from the digit at tenth place.

By putting the bars, 51.84 can be written as.

Step 2

Here, the smallest number is 7 whose square is less than 51. Taking 7 as the divisor and the first digit of the quotient, and 51 as the dividend, we obtain 2 as the remainder as shown below.

Step 3

Now, we place the decimal in the quotient as 84 is the decimal part, and bring down the number under the next bar to the right of the remainder.

Here, the number under the next bar is 84. The remainder obtained in the previous step is 2. Combining these numbers, we obtain the new dividend as 284 as shown below.

Step 4

Now, we double the previous divisor and enter it with a blank on its right.

Here, the divisor is 7. By making it double, we obtain 7 × 2 = 14. By putting a blank on the right side of 14, we obtain 14_.

Step 5

Now, we try to find the largest possible digit to fill the blank which also becomes the new digit of the quotient such that when the new digit is multiplied to the new divisor, the product should be less than or equal to the dividend.

Here, if we put 2 at the blank (14_), then the new digit of the quotient is 2 and the new divisor 142. By multiplying these two, we obtain 142 × 2 = 284. This is equal to the dividend.

Here, the remainder is 0 and no digit is left at the given number.

Regards