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julia_copen

  • 3 years ago

Can someone help me with this radical?

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  1. julia_copen
    • 3 years ago
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    \[\frac{ 7 }{ \sqrt{45} }\]

  2. anonymous
    • 3 years ago
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    hmmm

  3. anonymous
    • 3 years ago
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    maybe before you do that, note that \(45=9\times 5\) and so \(\sqrt{45}=\sqrt{9\times 5}=\sqrt{9}\sqrt{5}=3\sqrt{5}\)

  4. anonymous
    • 3 years ago
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    then \[\frac{ 7 }{ \sqrt{45} }=\frac{7}{3\sqrt{5}}\]and now you only need to multiply top and bottom by \(\sqrt{5}\) to remove the radical from the denominator

  5. anonymous
    • 3 years ago
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    @julia_copen you got this or you need the steps?

  6. julia_copen
    • 3 years ago
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    Steps please.

  7. anonymous
    • 3 years ago
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    lets start with \[\frac{7}{3\sqrt{5}}\] your job is to get the radical out of the denominator, so multiply top and bottom by \(\sqrt 5\) you get \[\frac{7}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}}{3\sqrt{5}\sqrt{5}}=\frac{7\sqrt{5}}{3\times 5}\]

  8. anonymous
    • 3 years ago
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    typo there, meant \[\frac{7}{3\sqrt{5}}\times \frac{\sqrt{5}}{\sqrt{5}}=\frac{7\sqrt{5}}{3\sqrt{5}\sqrt{5}}=\frac{7\sqrt{5}}{3\times 5}\]

  9. anonymous
    • 3 years ago
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    final answer is \(\frac{7\sqrt{5}}{15}\)

  10. anonymous
    • 3 years ago
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    another quick example \[\frac{4}{\sqrt{3}}=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{4\sqrt{3}}{3}\]

  11. julia_copen
    • 3 years ago
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    Thanks so much! Me and my friend were having a hard time trying to understand how to break it down.

  12. anonymous
    • 3 years ago
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    yw

  13. julia_copen
    • 3 years ago
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    can you help me with another?

  14. anonymous
    • 3 years ago
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    sure

  15. julia_copen
    • 3 years ago
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    \[\frac{ 1 }{ \sqrt{75z} }\]

  16. anonymous
    • 3 years ago
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    is the \(z\) inside the radical?

  17. julia_copen
    • 3 years ago
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    yes

  18. anonymous
    • 3 years ago
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    ok the idea is to see if the number is the product of some "perfect square" so in this case \(75=25\times 3\) making \[\sqrt{75}=\sqrt{25}\sqrt{3}=5\sqrt{3}\] so star with \[\frac{1}{5\sqrt{3z}}\] and then multiply top and bottom by \(\sqrt{3z}\)

  19. anonymous
    • 3 years ago
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    you get \[\frac{1}{5\sqrt{3z}}\times \frac{\sqrt{3z}}{\sqrt{3z}}=\frac{\sqrt{3z}}{15z}\]

  20. julia_copen
    • 3 years ago
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    Okay I see. It's always difficult in the beginning for me.

  21. anonymous
    • 3 years ago
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    you will get used to it, (and then probably forget it because it is not really that useful) but in any case it gets easier

  22. julia_copen
    • 3 years ago
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    Are you still on?

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