Solve the equation. Express numbers in exact simplest form. $$ 9 n^{2}=1 $$ The solution set is $$ \{\square\} $$.

Question

UpStudy AI · Accepted Answer

1. Divide both sides of the equation by 9:
   $$
   n^2 = \frac{1}{9}
   $$

2. Take the square root of both sides:
   $$
   n = \pm \sqrt{\frac{1}{9}}
   $$

3. Simplify the square root:
   $$
   \sqrt{\frac{1}{9}} = \frac{1}{3}
   $$

4. Thus, the solutions are:
   $$
   n = \frac{1}{3} \quad \text{and} \quad n = -\frac{1}{3}
   $$

The solution set is $$ \left\{-\frac{1}{3}, \frac{1}{3}\right\} $$.
The solutions are $$ n = \frac{1}{3} $$ and $$ n = -\frac{1}{3} $$.

Solve the equation. Express numbers in exact simplest form. \[ 9 n^{2}=1 \] The solution set is \( \{\square\} \).