Question

rationalise 3/4-root7

Answer 1

$\frac{3}{4 - \sqrt{7} } = \frac{3}{4 - \sqrt{7} } \times \frac{4 + \sqrt{7} }{4 + \sqrt{7} } \\ = \frac{3(4 + \sqrt{7} )}{(4) {}^{2} - ( \sqrt{7} ) {}^{2} } = \frac{12 + 3 \sqrt{7} }{16 - 7} \\ = \frac{12 + 3 \sqrt{7} }{9} = \frac{12}{9} + \frac{3 \sqrt{7} }{9} \\ = \frac{4}{3} + \frac{ \sqrt{7} }{3} = \frac{4 + \sqrt{7} }{3}$