Question

Rationalize 4+3√5 / 4-3√5

Answer 1

(4+3√5)*(4+3√5)/(4-3√5)*(4+√5)

(4+3√5)^2/4^2-(3√5)^2

16+45+24√5/16-45

61+24√5/29

Answer 2

Your answer is ---


we have

$\frac{4 + 3 \sqrt{5} }{4 - 3 \sqrt{5} } \\ \\ = \frac{(4 + 3 \sqrt{5} )(4 + 3 \sqrt{5} )}{(4 - 3 \sqrt{5}) (4 + 3 \sqrt{5} ) } \\ \\ = \frac{ {(4 + 3 \sqrt{5} )}^{2} }{ {4}^{2} - {(3 \sqrt{5} )}^{2} } \\ \\ = \frac{16 + 45 + 24 \sqrt{5} }{16 - 45} \\ \\ = \frac{61 + 24 \sqrt{5} }{ - 29} \\ \\ = - \frac{61 + 24 \sqrt{5} }{29}$