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CoffeeEyes

  • 3 years ago

Help? Please? 4/ 5 + √2

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  1. PhoenixFire
    • 3 years ago
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    What do you want done?

  2. CoffeeEyes
    • 3 years ago
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    I need to rationalize the denominator. I have no idea what the steps are. I read my text book, but I'm so confused.

  3. tkhunny
    • 3 years ago
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    Is it \[\frac{4}{5+\sqrt{2}}\]

  4. PhoenixFire
    • 3 years ago
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    \[4 \over {5+\sqrt{2}}\] so you multiply both the numerator and denominator by the conjugate of the denominator. \[5+\sqrt{2}\] conjugate is \[5 - \sqrt{2}\] so you get \[(5+\sqrt{2})(5-\sqrt{2})\] and as you know \[(a+b)((a-b)=a^2-b^2\] So the denominator becomes \[5^2-(\sqrt{2})^2=25-2=23\] Leaving you with \[{{4(5-\sqrt{2})} \over 23}={{20-4 \sqrt{2}} \over 23}\]

  5. tkhunny
    • 3 years ago
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    @op Please do a little better with your notation if this is correct. If you mean the expression that has been the target of this worked exercise, you have not written wat you intended. 4 / 5 + sqrt(2) = \[\frac{4}{5}+\sqrt{2}\] 4 / (5 + sqrt(2)) = \[\frac{4}{5+\sqrt{2}}\] Always remember your Order of Operations. Use parentheses to clarify meaning.

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