1.

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

Answer»

\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 }


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