Question

ms.sue, how would you solve the square-root of two manually, without a calculator?

Answer 1

I don't know. But this site explains how to do square root manually.

http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Answer 2

Newton's method.

Estimate the square root.
Divide the estimate into the original number. Then look at the result. If it is higher than the estimate, go half way of the difference an repeat.

Example: sqrt 25
estimate:4
25/4=6.25

half way between 4 and 6.25 is 5.13

25/5.13=4.87
halfway is 5.
25/5=5 Bingo.

Answer 3

another example: sqrt 136
estimate 12;
136/2=11.3
half way...11.7
136/11.7 = 11.6
half way: 11.65
136/11.65=11.67
half way: 11.66
136/11.66=11.66 Bingo.