આપેલ સંખ્યાઓનાં છેદનું સંમેયીકરણ કરો :

$(i)$ $\frac{1}{\sqrt{7}}$

$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}$

$(iii)$ $\frac{1}{\sqrt{5}+\sqrt{2}}$

$(iv)$ $\frac{1}{\sqrt{7}-2}$

$(i)$ $\frac{1}{\sqrt{7}} =\frac{1}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}}$ $=\frac{\sqrt{7}}{7} $

$(ii)$ $\frac{1}{\sqrt{7}-\sqrt{6}}=\frac{1}{\sqrt{7}-\sqrt{6}} \times \frac{\sqrt{7}+\sqrt{6}}{\sqrt{7}+\sqrt{6}}$

       $=\frac{\sqrt{7}+\sqrt{6}}{7-6}$ $=\frac{\sqrt{7}+\sqrt{6}}{1}$    $=\sqrt{7}+\sqrt{6}$

આમ, $\frac{1}{\sqrt{7}-\sqrt{6}}=\sqrt{7}+\sqrt{6}$

$(iii)$ $ \frac{1}{\sqrt{5}+\sqrt{2}} =\frac{1}{\sqrt{5}+\sqrt{2}} \times \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}$

$=\frac{\sqrt{5}-\sqrt{2}}{5-2}$

$=\frac{\sqrt{5}-\sqrt{2}}{3}$

આમ, $\frac{1}{\sqrt{5}+\sqrt{2}}=\frac{\sqrt{5}-\sqrt{2}}{3}$

$(iv)$ $\frac{1}{\sqrt{7}-2} =\frac{1}{\sqrt{7}-2} \times \frac{\sqrt{7}+2}{\sqrt{7}+2} =\frac{\sqrt{7}+2}{7-4} =\frac{\sqrt{7}+2}{3}$

આમ, $\frac{1}{\sqrt{7}-2}=\frac{\sqrt{7}+2}{3}$