How do I perform these functions without using a calculator?

Altrepair
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Anyone know of books or websites that teach one how to find square roots, cube roots, sin, cosine, e, ln, pi and so forth without using a calculator because this stuff is not taught in schools, but instead is simply calculated with calculators which is not what I like considering taking things for advantage is never wise.
 
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you could use a slide rule.
 
cragar said:
you could use a slide rule.

Or crayons and a ruler.
 
Right, they won't let me have sharp things like pencils.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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