Square Root of an Odd Powered Integer is Always Irrational?

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  • Thread starter e2m2a
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  • #26
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I'd like to deposit " " in my bank account please. That should be free, right?
 
  • #27
Nugatory
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However, floating point has exact and predictable behavior.
Yes, although that statement might easily be misunderstood by someone who hasn’t been through the wars. As many pre-IEEE floating point designs demonstrated, “exact and predictable” does not preclude “bizarre and surprising”.

IEEE-754 is one of the underappreciated triumphs of computing, making the world safer for the naive every day.
 
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  • #28
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The nth root of x given by =int(x^(1/n)) in Excel is an integer ;)
 
  • #29
jbriggs444
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The nth root of x given by =int(x^(1/n)) in Excel is an integer ;)
Are you suggesting something like...

Put some positive integer into A1
Put some positive integer into A2
Put =A1^A2 into A3
Put =INT(A3^(1/A2)) into A4
Observe that A4 is equal to A1 unless an overflow has occurred while computing A3
 
  • #30
BWV
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Are you suggesting something like...

Put some positive integer into A1
Put some positive integer into A2
Put =A1^A2 into A3
Put =INT(A3^(1/A2)) into A4
Observe that A4 is equal to A1 unless an overflow has occurred while computing A3
It was just an attempt at a joke, but per the OP x would be a^some odd power and n would be 1/2
 
  • #31
Baluncore
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From the research I have done since posting, it says that the square root of any non-square integer is always an irrational number.
Did you notice that if you write any of those irrational square roots as a continued fraction, they always repeat.
 

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