Find the square root of the following decimal number

Square root of a perfect square rational
number in the form of a decimal number:

We can directly find the square root of a
decimal number by division method without converting it into a rational number.

To find the square root of a decimal number
by division method proceed as follows:

1.     
Place bars on the integral part
of the given decimal number place in the usual manner.

2.     
Place bars on the decimal part
on every pair of digits beginning with the first decimal place. The number of
digits after the decimal point will be even if the number is a perfect square.

3.     
Start finding the square root
by the division method as usual.

4.     
Put the decimal point in the
square root as soon as internal part is exhausted.

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Finding square root by division method

Step 1 Place  bars  over every pair of digits starting from the
digit at one’s place. If the number of digits in it is odd, then the left-most
single digit too will have a bar.

Step 2 Find the largest number whose square is less than or equal to the
number under the extreme left bar. Take this number as the divisor and the
quotient with the number under the extreme left bar as the dividend.

Step 3 put the quotient above the number under the leftmost bar and write
the product of the divisior and the quotient just below this number.

Step
4

Subtract
the product of the divisor and the quotient from the number under the left most
bar and bring down the number under the next bar to the right of the remainder.
This becomes the New Dividend.

Step 5 Double the quotient and enter it with a blank space on the right for
the next digit of the next possible divisior.


Step 6 Guess a largest possible digit to fill the blank stated in step 5
in such a way that the product of the new divisior and this digit is  equal to or just less than the New Dividend  obtained in step 4 .

Step 7

Subtract
the product of the digit chosen in step 6 and the new divisior from the
dividend obtained in step 4 and bring down the number under the next bar to the
right of the new remainder. This becomes the  second New Dividend.

Step
8

Repeat
step 5 , step 6 and step 7 till all the bars have been taken up. The final quotient
is the required square root.

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Solution is in the attachment

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Hope his will help you...