MFACCT-001
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- Aug 17, 2020
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10 raised to (3/7) power by calculator yields a non-repeating, 15-digit (calculator limit) result: is this a rational or irrational number?
SEE HEREI was hoping that someone could verify that 10 raised to the (3/7) power is (or is not) a rational number. Your investigation (nice work) extended the calculated result to (31) decimals, showing a non-ending condition or repeating pattern. Perhaps there's a proof or other method to verify the computed result is rational (or irrational).
I believe tkhunny was suggesting the beginning of a way to prove that it is or is not irrational, similar to the proof that the square root of 2 is irrational. At the same time, that suggests that it is at least very likely that this, too, is irrational. To make that definite, you can either do the proof, or look it up (like pka), or look for a general theorem that applies.I was hoping that someone could verify that 10 raised to the (3/7) power is (or is not) a rational number. Your investigation (nice work) extended the calculated result to (31) decimals, showing a non-ending condition or repeating pattern. Perhaps there's a proof or other method to verify the computed result is rational (or irrational).
10^(3/7) = (10^3)^(1/7) = 1000^(1/7) Is that rational? What have you tried? Where did you get stuck? We are a math help forum where we prefer to help students solve their own problems vs just giving out the answer (which someone did do anyways).10 raised to (3/7) power by calculator yields a non-repeating, 15-digit (calculator limit) result: is this a rational or irrational number?