On Wednesday, November 8, 2017 at 3:12:45 AM UTC-5, bassam king karzeddin wrote: > 1) How can you approximate the arithmetical cube root of say (10) without using the decimal notation, (.), in any number system, say simply 10base number system? > > 2) What ultimately that you must discover about the arithmetical exact cube root of (10) but again without using the decimal notation? >
There is nothing wrong with decimal notation. Only a crank and a troll like BKK here could take exception. (He actually believes that 40 degree angles don't exist!)
Here is the cube root of 2 to 31 decimal places (32 significant digits):
1.259 921 049 894 873 164 767 210 607 278 2
Cube it and you will get:
1.999 999 999 999 999 999 999 999 999 999 9
Not close enough? You can get as close as you want, just never precisely 2. Just keep calculating more and more decimal places until the required accuracy is obtained. So, it makes sense to talk about the cube root of 2 as a real number and that you can add, subtract, multiply and divide such numbers.
If you want to know all the details, take a university course in introductory real analysis (a very challenging course, usually in 2nd year of pure math).