Question

Ratinalise 3-root 5 upon 3+2root5

Answer 1

[tex]\mathfrak{\huge{Answer:-}} \\ \bold{\frac{3 - \sqrt{5} }{3 + \sqrt{5} } } \\ = \frac{3 - \sqrt{5} }{3 + \sqrt{5} } \times \frac{3 - \sqrt{5} }{3 - \sqrt{5} } \\ = \frac{(3 - \sqrt{5})(3 - \sqrt{5} ) }{(3 + \sqrt{5} )(3 - \sqrt{5}) } \\ = \frac{ {(3 - \sqrt{5} )}^{2} }{ {(3)}^{2} - {( \sqrt{5} )}^{2} } \\ = \frac{9 + 5 - 6 \sqrt{5} }{9 - 5} \\ = \frac{14 - 6 \sqrt{5} }{4} \\ = \frac{2(7 - 3 \sqrt{5}) }{4} \\ = \frac{7 - 3 \sqrt{5} }{2} \\ \boxed{\boxed{\large{\bold{ \frac{3 - \sqrt{5} }{3 + \sqrt{5}} = \frac{7 - 3 \sqrt{5} }{2} }}}}[/tex]