Question

Rationalize the denominator of the following root 3 - root 1 upon root 3 + 1

Answer 1

$\frac{ \sqrt{3} - \sqrt{1} }{ \sqrt{3} + 1} \\ \\ = \frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1} \\ \\ = \frac{( { \sqrt{3} - 1})^{2} }{( \sqrt{3} + 1)( \sqrt{3} - 1)} \\ \\ = \frac{( { \sqrt{3}) }^{2} + 2 \times \sqrt{3} \times 1 - {1}^{2} }{( { \sqrt{3} )}^{2} - {1}^{2} } \\ \\ = \frac{9 + 2 \sqrt{3} - 1}{9 - 1} \\ \\ = \frac{8 + 2 \sqrt{3} }{8}$

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