Question

rationalise the denominator of 2/10√3 and 1/5+√6 and 7/2-√7​

Answer 1

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Answer 2

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$1. \: \frac{2}{10 \sqrt{3} } \\ \\ = \frac{2 \times 10 \sqrt{3} }{10 \sqrt{3} \times 10 \sqrt{3} } \\ \\ = \frac{20 \sqrt{3} }{300} \\ \\ = \frac{ \sqrt{3} }{15} \\ \\ 2. \: \frac{1}{5 + \sqrt{6} } \\ \\ = \frac{1 \times( 5 - \sqrt{6} )}{(5 + \sqrt{6} ) \times (5 - \sqrt{6} )} \\ \\ = \frac{5 - \sqrt{6} }{ {5}^{2} - { (\sqrt{6}) }^{2} } \\ \\ = \frac{5 - \sqrt{6} }{25 - 6} \\ \\ = \frac{5 - \sqrt{6} }{19} \\ \\ 3. \: \frac{7}{2 - \sqrt{7} } \\ \\ = \frac{7 \times (2 + \sqrt{7} )}{(2 - \sqrt{7}) \times (2 + \sqrt{7} )} \\ \\ = \frac{14 + 7 \sqrt{7} }{ {2}^{2} - {( \sqrt{7} )}^{2} } \\ \\ = \frac{7(2 + \sqrt{7} )}{4 - 7} \\ \\ = \frac{7(2 + \sqrt{7} )}{ - 3} \\ \\ = - \frac{7(2 + \sqrt{7} )}{3}$

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