simplify radical expressions using conjugates - simplify \frac{6 +\sqrt{3}} {4 - \sqrt{3}}

Sangeetha Pulapaka (last edited 3 years ago) (Expert, Educator @Qalaxia)

STEP 1: Recall what is a radical

STEP 2: Recall what is a radical expression

STEP 3: Recall what are conjugates in a radical expression

STEP 4: Simplify

\frac{6+\sqrt{3}}{4-\sqrt{3}}

\frac{6+\sqrt{3}}{4-\sqrt{3}}.\frac{4+\sqrt{3}}{4+\sqrt{3}}

= \frac{24+6\sqrt{3}+4\sqrt{3}+3}{16+4\sqrt{3}-4\sqrt{3}-3} =

\frac{27+10\sqrt{3}}{13}