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anonymous

  • 4 years ago

Simplify the following radicals by rationalizing the denominators.

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  1. anonymous
    • 4 years ago
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    one sec i am posting it.

  2. anonymous
    • 4 years ago
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    \[ \frac{x-y}{\sqrt{x}+\sqrt{y}} \]

  3. 2bornot2b
    • 4 years ago
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    \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\]\[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]

  4. 2bornot2b
    • 4 years ago
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    Now multiply those, you will have removed the radical sign from the denominator.

  5. anonymous
    • 4 years ago
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    how do i multiply them?

  6. 2bornot2b
    • 4 years ago
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    |dw:1328019438214:dw|

  7. anonymous
    • 4 years ago
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    Then i simplify? or no?

  8. 2bornot2b
    • 4 years ago
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    Actually you don't need to multiply the numerator, \[\frac{\cancel{(x-y)}({\sqrt{x}-\sqrt{y}})}{\cancel{x-y}}\]

  9. anonymous
    • 4 years ago
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    So all you have to do is multiply the denominator and that will be the answer?

  10. 2bornot2b
    • 4 years ago
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    In all similar problems as this one, just multiply the numerator and the denominator with the conjugate of the denominator, just as I did. And then you need to simplify. But in this problem, one of the terms of the numerator gets cancelled. Did you understand?

  11. 2bornot2b
    • 4 years ago
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    Did I puzzle you? Should I write down the whole thing again, in a concise way?

  12. anonymous
    • 4 years ago
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    You puzzled me sorry haha :/ I am terrible at math.

  13. 2bornot2b
    • 4 years ago
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    Ok, then I am writing down the whole thing in a better way....

  14. 2bornot2b
    • 4 years ago
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    You were given with the following expression \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\] right?

  15. anonymous
    • 4 years ago
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    Correct.

  16. 2bornot2b
    • 4 years ago
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    Now I multiply both the numerator and the denominator with the conjugate of the dimnomnator i.e. \[\sqrt{x}-\sqrt{y}\] So the expression gets converted to \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]

  17. 2bornot2b
    • 4 years ago
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    Is it clear till this step? I can multiply something to the numerator and as well as to the denominator since they can be cancelled Is it clear?

  18. anonymous
    • 4 years ago
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    Yes it is clear. I just do not know how to multiply correctly?

  19. 2bornot2b
    • 4 years ago
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    So now I can say \[\frac{x-y}{\sqrt{x}+\sqrt{y}}\times\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}-\sqrt{y}}\]\[=\frac{(x-y)({\sqrt{x}-\sqrt{y}})}{\sqrt{(x)^2}+\sqrt{(y)^2}}\]\[=\frac{\cancel{(x-y)}({\sqrt{x}-\sqrt{y}})}{\cancel{x-y}}\]

  20. anonymous
    • 4 years ago
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    so the answer is the last part of that problem?

  21. 2bornot2b
    • 4 years ago
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    The answer is \[\sqrt{x}-\sqrt{y}\]

  22. anonymous
    • 4 years ago
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    oh sorry didn't mean to put () and that is simpler then it looks i guess i was just over thinking it.

  23. 2bornot2b
    • 4 years ago
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    Did you understand?

  24. anonymous
    • 4 years ago
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    yes i did thanks!

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