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Saiyan

  • one year ago

I need help with this problem trying to figure out how to do it, plz help. I will give medal.

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  1. Saiyan
    • one year ago
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  2. Saiyan
    • one year ago
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    help plz

  3. Saiyan
    • one year ago
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    @phi

  4. phi
    • one year ago
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    if you have a "cube root" then if you multiply it by itself *three times* , you "get rid" of the the radical when they say "rationalized denominator" it means get rid of the radical in the bottom part of the fraction so to do that, multiply the bottom by \(\sqrt[3]{6} \sqrt[3]{6} \) and to keep things equal , you have to multiply the top by the same thing you get \[ \frac{\sqrt[3]{2} \sqrt[3]{6} \sqrt[3]{6} }{\sqrt[3]{6} \sqrt[3]{6} \sqrt[3]{6} } \]

  5. phi
    • one year ago
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    by definition, the bottom becomes 6 (the cube root multiplied three times undoes the radical)

  6. Saiyan
    • one year ago
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    Why would you multiply the numerator and the denominator twice by the denominator

  7. Saiyan
    • one year ago
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    oh ok

  8. Saiyan
    • one year ago
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    because it is cubed

  9. phi
    • one year ago
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    in the top, all three are cube roots so you can combine the top into \[ \sqrt[3]{2\cdot 6 \cdot 6} \] I would factor the 6 into 2*3 so we can write the top as \[ \sqrt[3]{2\cdot 2 \cdot 3 \cdot 2 \cdot 3} \] or reordering to make it clearer \[ \sqrt[3]{2\cdot 2 \cdot 2 \cdot 3 \cdot 3} \] now if we find *three of the same term* inside a cube root. we can "pull them out" and replace them with 1 term on the outside \[2 \sqrt[3]{3\cdot 3} \] so far we have \[ \frac{2 \sqrt[3]{3\cdot 3}}{6} \]

  10. Saiyan
    • one year ago
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    nvmd

  11. Saiyan
    • one year ago
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    and then multiply the 3's on the inside of the radical

  12. phi
    • one year ago
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    can you finish? we can't do much with the 3's inside (we would need 3 of them to simplify) so I would make them 9 and of course we can simplify 2/6 on the outside

  13. Saiyan
    • one year ago
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    so it would be A.

  14. phi
    • one year ago
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    yes

  15. Saiyan
    • one year ago
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    ok I understand how to do it now thankyou very much

  16. phi
    • one year ago
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    yw

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