Question

What is the root of 345 without the use of tables?

Answer 1

345 = 3*5*23, so no perfect squares

So, what methods of solution have you been given? The value will have to be an approximation, so use some numerical method or graphical method to get the value.

interpolation, Newton's method, bisection, or something else.

Answer 2

"without the use of tables" ??
- then how about just using a calculator ? ( I am being facetious)


Here is the method I actually taught in medieval times, and remember we had no calculators either.

http://www.johnkerl.org/doc/square-root.html