prove ..

$$\frac{1}{\sqrt2}\\\\
=\frac{1\times \sqrt2}{\sqrt2\times \sqrt2}\\\\
=\frac{\sqrt2}{2}\\\\\\
or\;alternatively\\\\
\frac{\sqrt2}{2}\\\\
=\frac{\sqrt2\div \sqrt2}{2\div \sqrt2}\\\\
=\frac{1}{2^1\div 2^{1/2}}\\\\
=\frac{1}{2^{1-(1/2)}}\\\\
=\frac{1}{2^{(1/2)}}\\\\
=\frac{1}{\sqrt2 }\\\\$$

melody !! You are gorgeous 

Thanks,

Flattery goes a long way with me