Calculating 3^0.2 without using a calculator?

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SUMMARY

The discussion centers on calculating 3^0.2 without a calculator, emphasizing the irrational nature of such calculations. Participants clarify that while integers with fractional exponents cannot be expressed as products of integers, logarithmic methods can be employed. Specifically, using natural logarithms, one can derive 3^0.2 by calculating ln(3) and manipulating it through logarithmic identities. Additionally, Newton's method is suggested as an effective iterative approach for approximating roots, demonstrating the mathematical principles involved in such calculations.

PREREQUISITES
  • Understanding of natural logarithms and their properties
  • Familiarity with irrational numbers and their definitions
  • Knowledge of Newton's method for root approximation
  • Basic arithmetic operations and manipulation of exponents
NEXT STEPS
  • Learn how to use logarithmic tables for manual calculations
  • Study Newton's method in detail for root finding
  • Explore the properties of irrational numbers and their implications
  • Investigate the Cordic method for calculating functions on calculators
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Mathematicians, students studying algebra and calculus, and anyone interested in manual calculation techniques for exponentiation and root finding.

  • #31
BobG said:
You're killing me, here. :smile:

I swear. People born after the invention of the electronic calculator have no appreciation for art.

Did you make your last assertion wrt to me??Learn that before putting my hand on a 'scientific' calculator (the one with radicals,trig.functions and logarithms),i worked both with a slide rule and with logarithm tables.I want to say that i found it more "challanging" working with the logarithm tables rather than slide rule,which is in fact some sort of calculator too...You don't make that calculation,the slide rule does.

Daniel.

PS.Actually,all the calculations are being made by the ones who computed the first logarithm tables.We're just taking advantage of their work...
 
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  • #32
dextercioby said:
Did you make your last assertion wrt to me??Learn that before putting my hand on a 'scientific' calculator (the one with radicals,trig.functions and logarithms),i worked both with a slide rule and with logarithm tables.I want to say that i found it more "challanging" working with the logarithm tables rather than slide rule,which is in fact some sort of calculator too...You don't make that calculation,the slide rule does.

Daniel.

PS.Actually,all the calculations are being made by the ones who computed the first logarithm tables.We're just taking advantage of their work...
I'm just kidding with you.

I just like slide rules, probably as much (if not more) for aesthetic reasons as for function (bamboo just has such a nice feel to it, you get a satisfaction beyond just an answer). Plus, a lot of them have a sense of history to them. And, considering the condition of a lot of the slide rules you come across, they give you something to tinker with to restore them to back to perfect operating condition (although, a couple seem frustratingly beyond restoration to mere functionality - gouges and warping can be pretty hard to undo).
 
  • #33
If I had these pieces of equipment I would try to use them but all I have is my scientific calculator.

The Bob (2004 ©)
 

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