Saiyan
  • Saiyan
I need help with this problem trying to figure out how to do it, plz help. I will give medal.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Saiyan
  • Saiyan
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Saiyan
  • Saiyan
help plz
Saiyan
  • Saiyan
@phi

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phi
  • phi
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 \[ \frac{\sqrt[3]{2} \sqrt[3]{6} \sqrt[3]{6} }{\sqrt[3]{6} \sqrt[3]{6} \sqrt[3]{6} } \]
phi
  • phi
by definition, the bottom becomes 6 (the cube root multiplied three times undoes the radical)
Saiyan
  • Saiyan
Why would you multiply the numerator and the denominator twice by the denominator
Saiyan
  • Saiyan
oh ok
Saiyan
  • Saiyan
because it is cubed
phi
  • phi
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 \[ \frac{2 \sqrt[3]{3\cdot 3}}{6} \]
Saiyan
  • Saiyan
nvmd
Saiyan
  • Saiyan
and then multiply the 3's on the inside of the radical
phi
  • phi
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
Saiyan
  • Saiyan
so it would be A.
phi
  • phi
yes
Saiyan
  • Saiyan
ok I understand how to do it now thankyou very much
phi
  • phi
yw

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