Question

9 class que chapter 1 number system give ans in picture​

Answer 1

$\frac{4}{ 2 + \sqrt{3} + \sqrt{7} } \\ \\ \frac{4}{(2 + \sqrt{3}) + \sqrt{7} }$

Rationalising Factor of (2+√3)+√7=(2+√3)-√7

$\frac{4(2 + \sqrt{3} - \sqrt{7} ) }{[(2 + \sqrt{3}) + \sqrt{7}][(2 + \sqrt{3} ) - \sqrt{7}] } \\ \\ \frac{4(2 + \sqrt{3} - \sqrt{7}) }{(2 + \sqrt{3}) {}^{2} - \sqrt{7} {}^{2} } \\ \\ \frac{4(2 + \sqrt{3} - \sqrt{7} )}{4 + 3 + 4 \sqrt{3} - 7} \\ \\ \frac{4(2 + \sqrt{3} - \sqrt{7} )}{7 - 7 + 4 \sqrt{3} } \\ \\ \frac{4(2 + \sqrt{3} - \sqrt{7} )}{4 \sqrt{3} } \\ \\ \frac{2 + \sqrt{3} - \sqrt{7} }{ \sqrt{3} } \\ \\ \frac{(2 + \sqrt{3} - \sqrt{7}) \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } \\ \\ \frac{2 \sqrt{3} + 3 - \sqrt{21} }{3}$

Answer 2

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