anonymous
  • anonymous
How would i simplify these radicals?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\sqrt[3]{16} + \sqrt[3]{54}\]
anonymous
  • anonymous
\[2(\sqrt[3]{40}) - \sqrt[3]{5}\]
anonymous
  • anonymous
\[5(\sqrt[3]{48}) - 2(\sqrt[3]{162})\]

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TuringTest
  • TuringTest
by factoring the numbers under the radicals
lgbasallote
  • lgbasallote
what are the indeces? 2? sorry..kinda hard to read...
TuringTest
  • TuringTest
at least that is a good first step
TuringTest
  • TuringTest
they are 3's
TuringTest
  • TuringTest
you can right-click to make it larger
TuringTest
  • TuringTest
so nicole, what is the prime factorization of 16 ?
anonymous
  • anonymous
2,2,2,2 ? so \[2^{4}\]
TuringTest
  • TuringTest
right now we want the cubed root of that so we want to break this up so we can recognize the powers of 3 so note that this is\[\sqrt[3]{2^3\cdot2}=2\sqrt[3]2\]make sense?
TuringTest
  • TuringTest
\[\sqrt[3]{16}=\sqrt[3]{2^4}=\sqrt[3]{2^3\cdot2}=\sqrt[3]{2^3}\cdot\sqrt[3]2=2\sqrt[3]2\]
anonymous
  • anonymous
how does \[\sqrt[3]{2^{3}\times 2} = \sqrt[3]{2^{3}}\] ? :S
TuringTest
  • TuringTest
it doesn't, read above more closely
TuringTest
  • TuringTest
\[\sqrt[3]{2^{3}\cdot 2} = \sqrt[3]{2^{3}}\cdot\sqrt[3]2\]
anonymous
  • anonymous
i meant \[\sqrt[3]{2^{3}} \times \sqrt[3]{2}\]
TuringTest
  • TuringTest
because powers (and therefor roots) are distributive over multiplication test it...
TuringTest
  • TuringTest
\[\sqrt{36}=\sqrt{4\cdot9}=\sqrt4\cdot\sqrt9=2\cdot3=6\]it's just true :)
anonymous
  • anonymous
oh okay, now i get it :) yeah that does make sense
TuringTest
  • TuringTest
so you now see how\[\sqrt[3]{16}=2\sqrt[3]2\]? if so try the next one\[\sqrt[3]{54}\]
anonymous
  • anonymous
\[\sqrt[3]{54} = \sqrt[3]{2 \times 3^{3}} = \sqrt[3]{2} \times \sqrt[3]{3} \] ? :S
anonymous
  • anonymous
\[= 3\sqrt[3]{2} \]
TuringTest
  • TuringTest
yes, nice :) now what is the final answer?
anonymous
  • anonymous
the final answer is \[5\sqrt[3]{2}\]
TuringTest
  • TuringTest
exactly :) good job
anonymous
  • anonymous
thanks ! :) i'll get back to yo on the other questions once i finish them.
TuringTest
  • TuringTest
You're welcome :)
anonymous
  • anonymous
\[2(\sqrt[3]{40}) - \sqrt[3]{5} \]\[= 2(\sqrt[3]{2^{3}\times 5}) - \sqrt[3]{5} \]\[= 2(2\sqrt[3]{5}) - \sqrt[3]{5} \]\[= 4\sqrt[3]{5} - \sqrt[3]{5} \]\[= 3\sqrt[3]{5} \] \[5(\sqrt[3]{48}) - 2(\sqrt[3]{162}) \]\[= 5(\sqrt[3]{2^{4} \times 3}) - 2(\sqrt[3]{3^{4} \times 2}) \]\[= 5(\sqrt[3]{2^{4}} \times \sqrt[3]{3}) - 2(\sqrt[3]{3^{4}} \times \sqrt[3]{2}) \]\[= 5(2\sqrt[3]{2} \times \sqrt[3]{3}) - 2(3\sqrt[3]{3} \times \sqrt[3]{2}) \]\[= 5(2\sqrt[3]{6}) - 2(3\sqrt[3]{6}) \]\[= 10\sqrt[3]{6} - 6\sqrt[3]{6} \]\[= 4\sqrt[3]{6}\]
anonymous
  • anonymous
wow that took a while for me to get on here. lol
anonymous
  • anonymous
did i take the right steps? :)
TuringTest
  • TuringTest
that looks perfect :D excellent job :)

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