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Spartan_Of_Ares

  • 2 years ago

what is the value of the expression sqrt(27)+sqrt(32)-sqrt(75)

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  1. Spartan_Of_Ares
    • 2 years ago
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    \[\sqrt(27)+\sqrt(32)-\sqrt(75)\]

  2. Spartan_Of_Ares
    • 2 years ago
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    @zaynahf if your not busy can you help me out?

  3. zaynahf
    • 2 years ago
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    Sure, i can! Do you know how to simplify radicals?

  4. Spartan_Of_Ares
    • 2 years ago
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    not really

  5. Spartan_Of_Ares
    • 2 years ago
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    >< ---

  6. zaynahf
    • 2 years ago
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    To simplify radicals, you have to try to find a perfect square that fits perfectly into the number. So for the first one: \[\sqrt{27}\] the biggest perfect square that can fit into it is 9. So, the inside would simplify to be: \[\sqrt{9 \times 3} = 3\sqrt{3}\]

  7. Spartan_Of_Ares
    • 2 years ago
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    so i can get \[\sqrt16X2 = 4\sqrt2 ?\]

  8. zaynahf
    • 2 years ago
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    Yeah! Now try the third one

  9. Spartan_Of_Ares
    • 2 years ago
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    \[\sqrt75 = \sqrt5X15 = 5\sqrt5?\]

  10. zaynahf
    • 2 years ago
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    No, since neither 15 nor 5 are perfect squares. Here are the perfect squares: 1,4,9,16,25,36,49,64,81,100....

  11. Spartan_Of_Ares
    • 2 years ago
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    so \[aaaannnnnd`im lost\]

  12. zaynahf
    • 2 years ago
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    lol i'll guide you through

  13. Spartan_Of_Ares
    • 2 years ago
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    ok

  14. zaynahf
    • 2 years ago
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    Ok since you want to get the biggest one that goes into there, start from the top of the list. Try seeing if 100 goes into 75 (obviously not), so just start from the smallest number after 75. 64,36,25,16,4,1. When you find the one that goes into 72, let me know.

  15. Spartan_Of_Ares
    • 2 years ago
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    64

  16. zaynahf
    • 2 years ago
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    64 goes into 75 evenly?

  17. Spartan_Of_Ares
    • 2 years ago
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    oh no 25

  18. zaynahf
    • 2 years ago
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    Good! Now what times 25 is 75?

  19. Spartan_Of_Ares
    • 2 years ago
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    3

  20. zaynahf
    • 2 years ago
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    So thats what goes under the radical: \[\sqrt{75}= \sqrt{25 \times 3}= 5\sqrt{3}\] Right?

  21. Spartan_Of_Ares
    • 2 years ago
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    ok what do i do now multiply them together?

  22. zaynahf
    • 2 years ago
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    \[3\sqrt{3}+4\sqrt{2}-5\sqrt{3}\] Is that what you have so far?

  23. Spartan_Of_Ares
    • 2 years ago
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    yes

  24. zaynahf
    • 2 years ago
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    There are only 2 with the same base radical, so you can only simplify those

  25. Spartan_Of_Ares
    • 2 years ago
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    so i get \[8\sqrt3+ 4\sqrt2\]

  26. zaynahf
    • 2 years ago
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    Remember, it's 3-5, not 3+5

  27. Spartan_Of_Ares
    • 2 years ago
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    -2√3+4√2

  28. Spartan_Of_Ares
    • 2 years ago
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    is that my final answer?

  29. zaynahf
    • 2 years ago
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    Perfect

  30. zaynahf
    • 2 years ago
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    Yes it is

  31. Spartan_Of_Ares
    • 2 years ago
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    thnxs so much ^_^ now i can sleep ... eh maybe

  32. zaynahf
    • 2 years ago
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    No problem! Let me know if you need other help

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