Question

Rationalise the denominator of 3+√5 / 3-√5

Answer 1

$\frac{3 + \sqrt{5} }{3 - \sqrt{5} } \\ \\ rationalise - - > \\ \\ = > \frac{3 + \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } \\ \\ = > \frac{ ({3 + \sqrt{5}) }^{2} }{ {(3)}^{2} - ( { \sqrt{5} )}^{2} } \\ \\ = > \frac{9 + 5 + 2(3)( \sqrt{5} )}{9 - 5} \\ \\ = > \frac{14 + 6 \sqrt{5} }{4} \\ \\ = > \frac{2(7 + 3 \sqrt{5} )}{4} \\ \\ = > \frac{7 + 3 \sqrt{5} }{2}$

Answer 2

Heya !!!



3+✓5 / 3 - ✓5


=> 3 + ✓5 / 3 - ✓5 × 3 + ✓5/ 3 + ✓5




=> ( 3 + ✓5) ( 3 + ✓5) / ( 3 - ✓5) ( 3 + ✓5)



=> ( 3 + ✓5)² / (3)² - ( ✓5)²



=> (3)² + ( ✓5)² + 2 × 3 × ✓5 / 9 -5



=> 9 + 5 + 6✓5 / 4



=> 14 + 6✓5/4


=> 2 ( 7 + 3✓5 ) /4


=> 7 + 3✓5/2



HOPE IT WILL HELP YOU...... :-)