0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Square roots close range approximation

102

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
102
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
3
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. A procedure for finding square roots of numbers close to familiar square roots. Dave Coulson, 2014
• 2. This procedure is based on the expansion for square roots close to 1. &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029; .... x1C x1C x1C x1Cx1x1 3 3 2 2 1 1 0 0 2 5 2 1 2 3 2 1 2 1 2 1 2 1 2 1 2 1 &#xF02B; &#xF02B; &#xF02B; &#xF02B; &#xF03D;&#xF02B;&#xF03D;&#xF02B; &#xF02D; &#xF02D; &#xF02D;
• 3. This procedure is based on the expansion for square roots close to 1. &#xF028; &#xF029; &#xF028; &#xF029; &#xF028; &#xF029;&#xF028; &#xF029; &#xF028; &#xF029;&#xF028; &#xF029;&#xF028; &#xF029; ...xxx1 x1x1 3 2 3 2 1 2 12 2 1 2 1 2 1 2 1 &#xF02B;&#xF02D;&#xF02D;&#xF02B;&#xF02D;&#xF02B;&#xF02B;&#xF03D; &#xF02B;&#xF03D;&#xF02B;
• 4. This procedure is based on the expansion for square roots close to 1. &#xF028; &#xF029; ...xxx1 x1x1 3 8 32 4 1 2 1 2 1 &#xF02B;&#xF02B;&#xF02D;&#xF02B;&#xF03D; &#xF02B;&#xF03D;&#xF02B;
• 5. This procedure is based on the expansion for square roots close to 1. &#xF028; &#xF029; x1 x1x1 2 1 2 1 &#xF02B;&#xF0BB; &#xF02B;&#xF03D;&#xF02B;
• 6. This procedure is based on the expansion for square roots close to 1. Similarly &#xF028; &#xF029; x1 x1x1 2 1 2 1 &#xF02B;&#xF0BB; &#xF02B;&#xF03D;&#xF02B; &#xF028; &#xF029; x1 x1x1 2 1 2 1 &#xF02D;&#xF0BB; &#xF02D;&#xF03D;&#xF02D;
• 7. Error &lt; 0.01%
• 8. Error ~ 0.01%
• 9. In general, for k between 0 and 0.5, This should be equal to N+k for a perfect square root &#xF0E0;
• 10. k can never be bigger than 0.5. &#xF0E0; Therefore error decreases with N. Relative error decreases (roughly) with N2. Therefore....
• 11. Blue is absolute error, Red is relative error. Relative error is never higher than 6% and very quickly reduces to less than 1%. The worst estimates occur when estimating square roots of numbers less than 4.
• 12. Greater accuracy can be achieved by referencing the squares of halves. Error 0.2%
• 13. [END] dtcoulson@gmail.com