#2**+8 **

There are probably many methods........you can read about a couple of them here......http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html

(Be sure to scroll to the bottom of the page for some links to others.....)

CPhill
Oct 17, 2014

#1**+5 **

i dont know i belive it would be very hard to do that though it would take a math wiz

thelonewolf
Oct 17, 2014

#2**+8 **

Best Answer

There are probably many methods........you can read about a couple of them here......http://mathforum.org/dr.math/faq/faq.sqrt.by.hand.html

(Be sure to scroll to the bottom of the page for some links to others.....)

CPhill
Oct 17, 2014

#3**+5 **

Yes, one approach is to use a divide and average approach.

Example: $$\sqrt{3}$$

Guess an approximate answer, say 2.

- Divide to obtain 3/2 = 1.5 and average to obtain (2 + 1.5)/2 = 1.75.
- Divide to obtain 3/1.75 = 1.71428 and average to obtain (1.75 + 1.71428)/2 = 1.73214
- Divide to obtain 3/1.73214 = 1.73196 and average to obtain (1.73214 + 1.73196)/2 = 1.73205

This is already close to the value provided by a calculator and becomes even more accurate if you use more decimal places and repeat the divide and average a few more times. This method was known for thousands of years.

Guest Oct 17, 2014