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anonymous

  • 5 years ago

rationalize the denominator 3+√3/4-√3

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  1. anonymous
    • 5 years ago
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    multiply the top and bottom by the conjugate of the denominator, which is 4+sqrt3 \[\frac{3+\sqrt{3}}{4-\sqrt{3}}*\frac{4+\sqrt{3}}{4+\sqrt{3}}=\frac{15+7\sqrt{3}}{13}\] (some "foiling" omitted)

  2. anonymous
    • 5 years ago
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    it is right but where did you get the 13 from??

  3. anonymous
    • 5 years ago
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    ok, that was part of the omitted foiling, which I'll now show. in the bottom we have \[(4-\sqrt{3})(4+\sqrt{3})=16+4\sqrt{3}-4\sqrt{3}-3=16-3=13\]

  4. anonymous
    • 5 years ago
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    on the roots cancelled out ...alrighty

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