Question

5) Rationalise:1/7-4 √3​

Answer 1

Answer

$= \frac{1}{7 - 4 \sqrt{3} } \\ \\ rationalising \: \: the \: \: denominator..... \\ \\ = \frac{1}{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ = \frac{7 + 4 \sqrt{3} }{ {(7)}^{2} - {(4 \sqrt{3} })^{2} } \\ \\ = \frac{7 + 4 \sqrt{3} }{49 - 16 \times 3} \\ \\ = \frac{7 + 4 \sqrt{3} }{49 - 48} \\ \\ = 7 + 4 \sqrt{3}$