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Here's an easy to follow page that will help...
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thats pretty cool. I've never seen that before. As for numbers other than the square root (like that other method wouldn't work) all i can think of is using logs. Like if you had a log table and anti-log tale, or a calculator with only log functions and no root function.
anyways for the example its:
27^(1/3) = x
(1/3)log27 = logx
note: log27 = 1.43 (this is what you'd look up)
(1/3)*1.43 = logx
0.48= logx
note: the anti log is just 10 to the power of a number ie 10^
you'd also look this up!
10^.48 = x
3 = x