Question

1/route 5 + route 2

rationalise
​

Answer 1

$\quad\frac{1}{\sqrt{5}+\sqrt{2}}\\\Rightarrow\frac{1}{(\sqrt{5}+\sqrt{2})}\times\frac{(\sqrt{5}-\sqrt{2})}{(\sqrt{5}-\sqrt{2})}\\\Rightarrow\frac{(\sqrt{5}-\sqrt{2})}{(\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})}\\\Rightarrow\frac{(\sqrt{5}-\sqrt{2})}{(\sqrt{5})^2-(\sqrt{2})^2}\qquad\quad\therefore\orange{(a+b)(a-b)=a^2-b^2}\\\Rightarrow\frac{(\sqrt{5}-\sqrt{2})}{5-2}\\\Rightarrow\frac{(\sqrt{5}-\sqrt{2})}{5-2}\\\Rightarrow\frac{(\sqrt{5}-\sqrt{2})}{5-2}\\\Rightarrow\bold{\frac{(\sqrt{5}-\sqrt{2})}{3}}$