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HorseCrazyGirlForever

  • 2 years ago

Solve the following roots. Please explain the steps.

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  1. HorseCrazyGirlForever
    • 2 years ago
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    \[\sqrt{54}\]

  2. HorseCrazyGirlForever
    • 2 years ago
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    \[\sqrt{60}\]

  3. jim_thompson5910
    • 2 years ago
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    I'll do the first one to get you started

  4. jim_thompson5910
    • 2 years ago
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    The idea is to factor the radicand into two factors where one factor is a perfect square (the largest perfect square possible)

  5. jim_thompson5910
    • 2 years ago
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    Then you break up the root and simplify

  6. jim_thompson5910
    • 2 years ago
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    \[\Large \sqrt{54} = \sqrt{9*6}\] \[\Large \sqrt{54} = \sqrt{9}*\sqrt{6}\] \[\Large \sqrt{54} = 3\sqrt{6}\]

  7. HorseCrazyGirlForever
    • 2 years ago
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    omg thank you so much!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

  8. jim_thompson5910
    • 2 years ago
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    yw

  9. HorseCrazyGirlForever
    • 2 years ago
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    So \[\sqrt{60}= 3\sqrt{10}\]

  10. jim_thompson5910
    • 2 years ago
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    no

  11. jim_thompson5910
    • 2 years ago
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    keep in mind that 60 = 4*15

  12. HorseCrazyGirlForever
    • 2 years ago
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    So the answer is \[2\sqrt{15}\]

  13. jim_thompson5910
    • 2 years ago
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    good

  14. HorseCrazyGirlForever
    • 2 years ago
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    YUS! Victory dance! Thank you so much! You are the most helpful person I have met on here! I cannot thank you enough! I was being made fun of for not being able to do these problems... You changed my life! Literally! Now I won't fail 7th grade! Thank you SO much again! I wish I could give you more medals!

  15. jim_thompson5910
    • 2 years ago
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    yw, glad to be of help

  16. HorseCrazyGirlForever
    • 2 years ago
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    So I am looking for the biggest possible number to go into it? Like \[\sqrt{64} = 2\sqrt{16}\]

  17. jim_thompson5910
    • 2 years ago
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    64 is a perfect square

  18. jim_thompson5910
    • 2 years ago
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    since 8^2 = 64 or 8*8 = 64

  19. jim_thompson5910
    • 2 years ago
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    so \[\Large \sqrt{64} = 8\]

  20. HorseCrazyGirlForever
    • 2 years ago
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    Ohhh ok! I get it now! Thank you SO much!

  21. jim_thompson5910
    • 2 years ago
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    np

  22. HorseCrazyGirlForever
    • 2 years ago
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    \[\sqrt{72}= 2\sqrt{18}\]

  23. jim_thompson5910
    • 2 years ago
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    find the largest perfect square that is a factor of 72

  24. jim_thompson5910
    • 2 years ago
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    the perfect squares (up to 100) are: 1,4,9,16,25,36,49,64,81,100

  25. HorseCrazyGirlForever
    • 2 years ago
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    So I have to use a perfect square every time?

  26. jim_thompson5910
    • 2 years ago
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    yes, you have to factor the number into two numbers where one number is the largest perfect square possible

  27. HorseCrazyGirlForever
    • 2 years ago
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    Wow! My mom could never explain as good as you do! lol! I will let you know if I need anymore help! :D Again, I cannot thank you enough! I will forever be in your debt!

  28. jim_thompson5910
    • 2 years ago
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    sure thing, again glad to be of help

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