Answer
{$- \frac{7\sqrt 3}{6}, \frac{7\sqrt 3}{6}$}
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: $12n^{2}=49$
Step 2: $n^{2}=\frac{49}{12}$
Step 3: $n=\pm \sqrt {\frac{49}{12}}$
Step 4: $n=\pm \frac{\sqrt {49}}{\sqrt {12}}$
Step 5: $n=\pm \frac{\sqrt {49}}{\sqrt {4\times3}}$
Step 6: $n=\pm \frac{7}{2\sqrt 3}$
Step 7: $n=\pm \frac{7}{2\sqrt 3}\times\frac{2\sqrt 3}{2\sqrt 3}$
Step 8: $n=\pm \frac{14\sqrt 3}{(2\sqrt 3)^{2}}$
Step 9: $n=\pm \frac{14\sqrt 3}{4 \times 3}$
Step 10: $n=\pm \frac{14\sqrt 3}{12}$
Step 11: $n=\pm \frac{7\sqrt 3}{6}$
The solution set is {$- \frac{7\sqrt 3}{6}, \frac{7\sqrt 3}{6}$}.
