I have wondered if irrational numbers could operate on irrational numbers to produce a rational number. How to find which two rational numbers will produce a rational number? Only one irrational number is needed and any rational number can be chosen.For two irrational numbers and one rational number: |

i1 X i2 = R |

So |

i1 X (R / i1) = Rπ X (5 / π) = 5π X 1.5915494309… = 5 |

Also |

2 ^{ 3 } = 8 |

so |

8 ^{1/3} =2 |

and |

(8 ^{1/3}) ^{3} = 8 |

So |

(13 ^{1/π}) ^{π} = 13 |

So |

2.2624509981… ^{ π } = 13 |

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