Question

simplify root 6 + root 4 / root 6 - root 4​

Answer 1

$\frac{ \sqrt{6} + \sqrt{4} }{ \sqrt{6} - \sqrt{4} } = \frac{( \sqrt{6} + \sqrt{4} )( \sqrt{6} + \sqrt{4} ) }{( \sqrt{6} - \sqrt{4} )( \sqrt{6} + \sqrt{4}) } \\ = \frac{6 + 2 \sqrt{4} \sqrt{6} + 4 }{6 - 4} = \frac{10 + 2 \sqrt{24} }{2} \\ = 5 + \sqrt{24} = 5 + \sqrt{6 \times 4} \\ = 5 + 2 \sqrt{6}$

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