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Melodious

  • one year ago

which is smaller 5 root 10 or 4 root 9?????????

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  1. anonymous
    • one year ago
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    You mean \(5\sqrt{10}\) or \(4\sqrt{9}\)? Observe that \(5>4\) and \(\sqrt{10}>\sqrt{9}\). Which do you think is larger?

  2. Melodious
    • one year ago
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    4 root 9 is larger right?

  3. anonymous
    • one year ago
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    No. Since 4<5 and sqrt9 < sqrt10, one would expect that 4sqrt9<5sqrt10, otherwise one would violate some variant of Archimedes' principle.

  4. Melodious
    • one year ago
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    can u simplify the roots and help me out @nettle404

  5. anonymous
    • one year ago
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    I think \(\sqrt{10}\) is about as simple as it can get. On the other hand, what squared gives you \(9\)?

  6. Melodious
    • one year ago
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    3

  7. anonymous
    • one year ago
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    Exactly, so \(\sqrt9=3\). But \(\sqrt{10}\) has no simple expression.

  8. Melodious
    • one year ago
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    but the question is 4 root 9 so it means 4 multiplied by root 9

  9. Melodious
    • one year ago
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    which is 3x4=12

  10. anonymous
    • one year ago
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    Yep.

  11. anonymous
    • one year ago
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    You got it.

  12. Melodious
    • one year ago
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    what about 5 root 10?

  13. anonymous
    • one year ago
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    Not easily simplified. Can you think of any way to square a number to obtain 10?

  14. zepdrix
    • one year ago
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    You can introduce another number like this if it helps you understand what is going on. \[\large\rm 4\sqrt9\lt5\sqrt9\]But also\[\large\rm 5\sqrt9\lt5\sqrt{10}\]So we see that\[\large\rm 4\sqrt{9}\lt5\sqrt9\lt5\sqrt{10}\]Therefore\[\large\rm 4\sqrt9\lt5\sqrt{10}\]

  15. zepdrix
    • one year ago
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    Maybe that's more complicated though :3 lol

  16. anonymous
    • one year ago
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    How about proof by contradiction? Suppose that \(5\sqrt{10}\leq4\sqrt{9}\), then \(5\sqrt{10}\leq12\) and \(\sqrt{10}\leq12/5\). Since \(\sqrt{10}>3\) but \(12/5<3\), we have \(3<3\), which is false.

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