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Lv 7
? asked in Science & MathematicsMathematics · 8 years ago

Fun which is larger: (ninth root of 9!) or (tenth root of 10!)?

I'm bored.

4 Answers

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  • Captain Matticus, LandPiratesInc
    Lv 7
    8 years ago
    Favorite Answer

    (9!)^(1/9) and (10!)^(1/10)

    Raise them both to the 90th power

    (9!)^10 and (10!)^9

    (9!)^10 =.= (10 * 9!)^9

    (9!)^10 =.= 10^9 * (9!)^9

    9! =.= 10^9

    We can tell, intuitively, that 9! < 10^9. Therefore, (9!)^(1/9) < (10!)^(1/10)

  • ?
    Lv 4
    4 years ago

    Tenth Root

    Source(s): https://owly.im/a89Hz
  • Fred
    8 years ago

    ninth root of 9! = 4.14716627...

    tenth root of 10! = 4.52872868...

    ∴ninth root of 9! < tenth root of 10!

  • L. E. Gant
    Lv 7
    8 years ago

    9^(1/9) > 10^(1/10)

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