Question

express 3+2√5/3-2√5 into the form of a number having the denominator as an integer

Answer 1

$\dfrac{3 + 2\sqrt{5}}{3 - 2\sqrt{5}}$

$= \dfrac{(3 + 2\sqrt{5}) \times (3 + 2\sqrt{5}) }{(3 - 2\sqrt{5}) \times (3 + 2\sqrt{5})}$

$= \dfrac{(3 + 2\sqrt{5})^2 }{ (3)^2 - (2\sqrt{5})^2 }$

$= \dfrac{(3 + 2\sqrt{5})^2 }{ 9 - 20 }$

$= -\dfrac{(3 + 2\sqrt{5})^2 }{ 11 }$