You may have incorrectly simplified the fraction to $\displaystyle\frac{{1}}{\sqrt{{{3}}}}\usepackage{cmbright}\Huge\$ and then rationalized that denominator. You could rewrite $\displaystyle\frac{\sqrt{{7}}}{{\sqrt{{21}}}}=\sqrt{{\frac{{7}}{{21}}}}=\sqrt{{\frac{{1}}{{3}}}}=\frac{\sqrt{{1}}}{\sqrt{{3}}}=\frac{{1}}{\sqrt{{3}}}\usepackage{cmbright}\Huge\$

This is not equal to $\displaystyle\frac{{7}}{\sqrt{{21}}}\usepackage{cmbright}\Huge\$