Answer
{$-\frac{4\sqrt 3}{3}, \frac{4\sqrt 3}{3}$}
Work Step by Step
Using Property 10.1, which states that for any non-negative real number $a$, $x^{2}=a$ can be written as $x=\pm\sqrt a$, we obtain:
Step 1: $3x^{2}=16$
Step 2: $x^{2}=\frac{16}{3}$
Step 3: $x=\pm \sqrt {\frac{16}{3}}$
Step 4: $x=\pm \frac{\sqrt {16}}{\sqrt 3}$
Step 5: $x=\pm \frac{4}{\sqrt 3}$
Step 6: $x=\pm \frac{4}{\sqrt 3}\times\frac{\sqrt 3}{\sqrt 3}$
Step 7: $x=\pm \frac{4\sqrt 3}{(\sqrt 3)^{2}}$
Step 8: $x=\pm \frac{4\sqrt 3}{3}$
The solution set is {$-\frac{4\sqrt 3}{3}, \frac{4\sqrt 3}{3}$}.
