Factor 48 so that you have a perfect square times a number with no square factors:

$\displaystyle\sqrt{{48}}=\sqrt{{{16}\cdot{3}}}=\sqrt{{{4}\cdot{4}\cdot{3}}}=\sqrt{{{{4}}^{{2}}\cdot{3}}}\usepackage{cmbright}\Huge\$

Use $\displaystyle\sqrt{{{a}{b}}}=\sqrt{{a}}\cdot\sqrt{{b}}\usepackage{cmbright}\Huge\$ to rewrite the expression: $\displaystyle\sqrt{{{{4}}^{{2}}\cdot{3}}}=\sqrt{{{{4}}^{{2}}}}\cdot\sqrt{{3}}\usepackage{cmbright}\Huge\$

Take the square root of $\displaystyle{{4}}^{{2}}\usepackage{cmbright}\Huge\$ : $\displaystyle{4}\sqrt{{3}}\usepackage{cmbright}\Huge\$