Question

rationalize in the form of A and B​

Answer 1

Step-by-step explanation:

$\frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \\ = \frac{5 + \sqrt{3} }{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ = \frac{(5 + \sqrt{3} )(7 + 4 \sqrt{3}) }{(7 - 4 \sqrt{3} )(7 + 4 \sqrt{3}) } \\ = \frac{(5 \times 7) + (5 \times 4 \sqrt{3}) + ( \sqrt{3} \times 7) + ( \sqrt{3} \times 4 \sqrt{3}) }{ {7}^{2} - {(4 \sqrt{3} )}^{2} } \\ = \frac{35 + 20 \sqrt{3} + 7 \sqrt{3} + 12}{49 - (16 \times 3)} \\ = \frac{47 + 27 \sqrt{3} }{49 - 48} \\ = 47 + 27 \sqrt{3}$

a = 1, b = 27