You may have incorrectly simplified the fraction to $\displaystyle\frac{{1}}{\sqrt{{{2}}}}\usepackage{cmbright}\Huge\$ and then rationalized that denominator. You could rewrite $\displaystyle\frac{\sqrt{{5}}}{{\sqrt{{10}}}}=\sqrt{{\frac{{5}}{{10}}}}=\sqrt{{\frac{{1}}{{2}}}}=\frac{\sqrt{{1}}}{\sqrt{{2}}}=\frac{{1}}{\sqrt{{2}}}\usepackage{cmbright}\Huge\$ . This is not equal to $\displaystyle\frac{{5}}{\sqrt{{10}}}\usepackage{cmbright}\Huge\$ .