Question

rationalise 4/2+route3+route7​

Answer 1

Answer:

$\frac{4}{2 + \sqrt{3} + \sqrt{7} } \\ \\ = \frac{4}{2 + \sqrt{3} + \sqrt{7} } \times \frac{2 - ( \sqrt{3} + \sqrt{7} )}{2 - ( \sqrt{3} + \sqrt{7} )} \\ \\ = \frac{4(2 - ( \sqrt{3} + \sqrt{7} ))}{4 - ( \sqrt{3} + \sqrt{7}) {}^{2} } \\ \\ = \frac{4(2 - ( \sqrt{3} + \sqrt{7} ))}{ - ( 6 + \sqrt{21} ) } \times \frac{6 - \sqrt{21} }{6 - \sqrt{21} } \\ \\ = \frac{4(2 - ( \sqrt{3} + \sqrt{7} ))(6- \sqrt{21}) }{ - (36 - 21) }$