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[Solved] Simplifying fraction roots

 
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June 15, 2021 10:21 am
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(@armor)
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Simplify  \frac{2\sqrt{6}-1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}.

 

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June 15, 2021 10:21 am
Topic starter
Staff 
(@armor)
Admin
  Honorable Member
317 Posts
156 153 0

Let   \large \sqrt{2}+\sqrt{3}=a,    and take square to obtain   \large 2\sqrt{6}=a^2-5,   thus

\large \frac{2\sqrt{6}-1}{\sqrt{2}+\sqrt{3}+\sqrt{6}}= \frac{a^2-5-1}{a+\sqrt{6}}

\large = \frac{(a+\sqrt{6})(a-\sqrt{6})}{a+\sqrt{6}}=a-\sqrt{6}=\sqrt{2}+\sqrt{3}-\sqrt{6} 

 

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