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anonymous

  • one year ago

Rationalize the denominator and simplify.

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  1. anonymous
    • one year ago
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  2. AbdullahM
    • one year ago
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    Hi, welcome to OpenStudy.

  3. anonymous
    • one year ago
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    thanks

  4. AbdullahM
    • one year ago
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    To rationalize the denominator, you must multiply the numerator and denominator by the conjugate of the denominator. What is the conjugate of \(\sqrt{a}-2\sqrt{y}\)?

  5. anonymous
    • one year ago
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    you would just switch the subtraction to addition right?

  6. anonymous
    • one year ago
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    how did you make that square root symbol

  7. AbdullahM
    • one year ago
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    It's called latex. `\(\sqrt{a}\)` That's the code to do it. You can also use the equation button to do it easier :)

  8. anonymous
    • one year ago
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    ok cool so wouldnt it be

  9. anonymous
    • one year ago
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    \[\sqrt{a}+2\sqrt{y}\]

  10. AbdullahM
    • one year ago
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    Correct!

  11. AbdullahM
    • one year ago
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    So now, lets do the multiplication. \(\Large\frac{\sqrt{a}+2\sqrt{y}}{\sqrt{a}-2\sqrt{y}}\times \frac{\sqrt{a}+2\sqrt{y}}{\sqrt{a}+2\sqrt{y}}=?\)

  12. AbdullahM
    • one year ago
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    Hint: \(\sf\Large (x+y)(x+y)=x^2+2xy+y^2\) \(\sf\Large (x+y)(x-y)=x^2-y^2\)

  13. anonymous
    • one year ago
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    you lost me

  14. AbdullahM
    • one year ago
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    Ok, lets multiply the numerators first. \(\sf\Large (\sqrt{a}+2\sqrt{y})\times (\sqrt{a}+2\sqrt{y})=?\)

  15. AbdullahM
    • one year ago
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    Use the formula I gave you above.

  16. anonymous
    • one year ago
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    \[\sqrt{a^2}+4\sqrt{y^2}\]

  17. anonymous
    • one year ago
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    ?

  18. AbdullahM
    • one year ago
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    No...

  19. AbdullahM
    • one year ago
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    \(\sf\Large (\sqrt{a}+2\sqrt{y})\times (\sqrt{a}+2\sqrt{y})=?\) Use the formula: \(\sf\Large (x+y)\times (x+y)= x^2+2xy+y^2\) remember: x, y, a, and b are all variables.

  20. anonymous
    • one year ago
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    im lost

  21. anonymous
    • one year ago
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    @Lyralei can you help me

  22. AbdullahM
    • one year ago
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    Where are you lost at?

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