**
EXTRACTING SQUARE ROOT FROM
DECIMAL NUMBER:**

** **Here the number is 53163214. We have
to extract the square root of this number. That’s why we divide the number in
groups of two. Here in last group 53 is left. And 49 is the nearest lowest square
number of 53. And it is square of 7. After that we multiply 2 with 7 and get
14.

Here N=53, and remainder is 53-49=4. Now the number becomes 41. We subtract 14*2=28 from 41. And get 13.

Here N=136, and the result is 2. We are not taking 7 in our calculation in this part. So duplex of 2 is 2*2=4. We subtract it from N to get the new value of N. So now N=136-4=132. And R=132-14*9 =132-126=6. We put 9 on result part.

Here N=63, and in the result part we get 29. So duplex of 29 is 2*2*9= 36. We subtract it from N to get the new value of N. So N = 63-36=27. And R=27-14*1=13. We put 1 in result part.

Here N=132, and in the result part we get 291. So duplex of 291 is 9*9+2*2*1=85. We subtract is from N to get new value of N. So N= 132-85=47. And R=47-14*3=47-42=5. We put 3 in the result part.

Here N=51, and in the result part we get 2913. So duplex of 2913 is 2*2*3+2*9*1=30. We subtract it from N to get new value of N. So N=51-30=21. And R=21-14*1=7. We put 1 in the result part.

Here N=74, and in the result part we get 29131. So duplex of 29131 is 1*1+2*9*3+2*2*1=59. We subtract it from N to get the new value of N. So N=74-59=15. And R=15-14=1. We put 1 in our result part.

Here we added a zero(0) after the number. So N=10. And in that way the iteration goes on.

We take 53163214 as the input number. This has 8 bits. So we put a decimal point after 8/2=4 bits.

So computed value=7291.311

And actual value =7291.310856